A Center Controller reported they had numerous airspace violations and possibly separation errors but could not keep track due the complexity of the sector caused by weather deviations and no Traffic Mangement or Supervisory action to regulate the flow of traffic.

Narrative

At approximately XA:05AM local time on Date I arrived at work and saw on our overhead weather display that there was a solid line of extreme precipitation that cut straight through the middle of our specialty West to East moving Eastward. Furthermore; as everyone in our area and management knew well in advance; this would be the busiest day of traffic for our area for the year because [sports event] ended the evening before and they were expecting a huge volume of departures of private jets as well as arrivals and departures of air carriers to flush the city of the sports fans. The facility had done briefings and created modified route structures for these departures and there were different arrival procedures for each of our 4 corner posts for departures and arrivals into the terminal area for the event. None of the planning took into account any of the common weather patterns for this Gulf Coast region and none of the routes were adjusted for this solid; impenetrable line of precipitation extending at least 200 miles to the east of the airport. The problem/failure I am reporting is far more widespread than just the East Arrival/Departure corridor; however; that is the sector I had my events with that day. Sectors involved in this issue were ZZZ1 (SECTOR XX); ZZZ2 (sector YY) and ZZZ3 (sector ZZ); ZZZ4 (ZHU sector AA 10;000 up to infinity with no ultra high sector above it).The ZZZ1 sector typically has East Departures that are sent out of the ZZZ5 terminal area on headings to the ESE and they send arrivals into the same terminal area Westbound on a single STAR called the ZZZZZ arrival. Normally; these two are separated laterally enough to be manageable; however; today the ZZZ1 sector AA was cut into 1/3 of the normal skinny East/West sector that it is. The Extreme line of precipitation split it in half north to south making flight impossible for departures or arrivals/Departures anywhere north of ZZZ6 VOR. In the XX/XX high altitude airspace; we had the same exact airspace constraints to the north in that none of this huge volume of corporate jets mixed with air carrier departures and opposite direction arrivals as well as other arrivals East bound to Pensacola Florida that have to be descended all the way from cruise altitude to 11;000 ft. through the same departure East traffic and Florida Panhandle traffic climbing Westbound opposite direction to the ZZZ5 departures and climbing through the West Bound arrivals. There was also a smattering of overflights both fast and slow coming through this exact same tiny strip of usable airspace with no effort by anyone in the building to force them further South into the ZZZ4 sector XX airspace in order to control the chaos. There were no military airspace limitations that would have prohibited someone from taking action to have ZJX send these aircraft Southwest bound in order to keep them out of this hazardously complex stream of aircraft.My part in it: I walked into work at XA:00am central and was told to get the controller out who was currently getting slammed at Combined sectors XX/XX. There was a CPC sitting in front of sector XX (the sector that would be working all of these arrivals and departures from ZZZ5 approach. He was patiently waiting for the XX/XX controller to be able to get a breath in to split the sector but it never happened. I observed as somewhat an 'extra set of eyes' up to the point where the sector became temporarily manageable for a split. Unfortunately; due to our low staffing numbers and the fact that management failed us to properly staff the area after numerous verbal complaints were aired days before this traffic event and prior to the weather report telling the facility that this was going to happen. This is a common problem and practice in our area where some of the supervisors gamble on staffing at the controllers expense by not properly staffing for the shifts. My Supervisor was one of them who could have made a difference that day but chose not to. Every Single supervisor on duty that day had an opportunity to make sure that we would have appropriate staffing and rest periods for this event but they failed to care enough to do so. The argument would likely be made that they tried to call in someone that morning but they already knew that it would be highly unlikely that anyone would answer their phone especially on a last-minute call during the busiest traffic day of the year for our area during an extreme weather event. So; they gambled and myself and the other controllers in the area as well as at ZJX that had to receive our poor service that day were the ones who suffered. One of our supervisor's who is was scheduled for overtime to work position that day but never did show up so that took yet another possible relief and recovery break away from the work force who desperately needed it that day. This isn't a plea for a normal break for an arbitrary 2 hour rule; this is a break that someone needed because their head was spinning after having an extraordinary amount of airspace deviations and near-deals.Back to the scenario. The XX/XX slowed down enough to get a briefing and the controller being relieved was physically and mentally spent. I sat down and tried to get settled in to the position which was now suited with the brand new slew-ball; wide angle scope and brand new visual settings and colors. Everything looked terrible and different from the way my scope has been set up for about 14 years in this particular specialty. The cursor moves differently and tracks differently. On the scope there are new visual distractions that we are trying to get used to such as highlighting an aircraft now puts a big box around the aircraft call sign and other information. Just add that to the 'complexity pile' if you will. Shortly after I sit down; the D-side and trainer decide to take an approved break and so I was left alone at this sector that had been blowing up since XB:30AM as reported by the other controllers. In short order; it did in fact blow up again. I yelled over for a D-side and got one in an acceptable amount of time but just in-time so that I didn't go down the crapper with weather deviations; point outs on our South boundary since we did not have enough of our own airspace to manage the departures without all of them penetrating into the ZZZ4 (XX) airspace.To complicate it more; New Orleans Approach control was launching aircraft with destinations and routes to the Northwest out the East gate south of the weather getting them stuck there for over 200 miles entering deep into another Center airspace where their flight plan did not go through. Of course; we were forced at the XX/XX sector to do a last minute re-route on these aircraft which likely immediately inflated the ZJX controllers numbers into the red category as well since they were not expecting them originally. Other aircraft destined to the Northeast were sent out to the SouthWest on garbage routes also needing manual entry and verbal amendments to the aircraft. To try and guess at a percentage; I feel that at least 75% or more of the departures coming out of their terminal area required us to enter and issue a new routing with different fixes to these aircraft; get an accurate readback while 'hot swapping' the arrivals for departures through a confined sliver of airspace. With the weather where it was; it was not possible to just let an arrival fly by the departure. They had to all be swapped out altitude wise. Everyone of them. I shouted over at Supervisor Name to let him know that the aircraft were all coming out on bad routes from ZZZ5 approach so he could call down there to stop that from happening. The answer I got back from him after he talked to them is that they were using approved routes for this particular event. Basically; they were screwing center and the aircraft getting them stuck on the south side of this line of weather just so that they could flush the airport. It is my understanding that they had been given something like 15 or 30 miles between departures at some point. I doubt seriously that this was accomplished but there definitely was no consideration given between ZZZ5 airport and neighboring new airport because my departure string east bound was coming out separated by no more than 7 miles each if I was lucky.For the first 30 to 60 minutes of this approximate 2 hour ordeal I was struggling with the ZZZ5 arrivals coming from ZJX because they were simply crossing our boundary at or below FL340. This made it nearly impossible to get them down through this arrival push opposite to them so after fighting it for awhile I turned around to the supervisor and told him to call ZJX and get these arrivals down. The result of that was a mediocre FL280 or below. These arrivals needed to be lower to fight this sustained departure string. FL240 would have worked with the occasional FL260 to swap out but FL280 made it far too complex with such a short distance to swap out these aircraft. Eventually; the weather pushed arrivals to a point about 10 miles south of ZZZ6 VOR so the arrivals were just barely in the XX airspace at this point. 100% of the departures would be in ZZZ (XX). I shut off the low altitude sector from leaving them wander aimlessly Northeast bound and told him they all need to be on East headings on departure to try and create a flow. It would have been nice if someone in TMU (Traffic management unit) or at our WS (Weather Service) desk would have done this for me in lieu of just watching me struggle to swap out altitudes; expediting 100% of departure climbs and 100% of arrival descents. Literally anything would have been better than what was left undone. In summary; I am certain that I had a plethora of airspace deviations during this 2 to 2.5 hour event. I could not get out of the sector to give a briefing due to the complexity of it. It was just one of those rare occasions where you are stuck till it is over. Why the sector wasn't split off during the lull or when it was building is absolutely mind boggling to me. I am relatively certain that it was due to just not having the staffing for it but that is for the ZHU internal investigation to determine. However; I wanted to say that in the 30+ years I have been doing ATC I have of course seen failures of the system and underwhelming protection of the sectors from time to time. This was the worst I have ever seen so far. I am ashamed of our facility from the facility manager through TMU down to our area supervisors for letting this happen to our controller workforce and these pilots. Safety was compromised this day without exception. How do I know that you ask? Because I am also ashamed of myself. I know better. I should have shut off ZJX myself and told them to keep the arrivals out of my airspace and then I should have dealt with the fallout on the backside for shutting them off instead of having uncounted deviations of airspace with sector XX; XX and ZJX30 and ZJX11 and guessing at separation on more times than I can count in one session. I saw no other way of doing the job that I was forced to do that day by our 'leadership' and for that I am ashamed of myself. The only thing I know for certain at this point is not if it will ever happen again (because I know it will). But it will never happen to me again. End rant.Now; what can be done about this in the future to prevent it you ask? The one thing that hind-sight tells me we need to establish internally immediately is some type of 'shelf' that can be requested from the ZZZ4 (XX) sector in their Northeast corner of their airspace that can be released to sectors XX (ZZZ1) and sector XX (ZZZ3). Possibly even release this to the ultra high 37 for uniformity. The Northeast corner of ZZZ4 is very seldom used airspace. A controller at sector XX in need of some extra space could simply call over to LEV and ask for the 'LEV shelf' which could internally be known to be a line that comes from the Z