B767 First Officer reported C hydraulic system failure resulted in special handling to landing with tow to gate.

Narrative

Briefing; preflight; and Ground Operations were unremarkable. We noted in Operations during briefing that there had been a write-up regarding an EICAS message - 'C Hyd Dem'. We discussed it briefly and noted that we would watch for any abnormalities.On takeoff; at gear retraction; we all noticed an increased odd noise from under the aircraft and also an unusual slight vibration. We did get a similar EICAS msg that illuminated briefly; but gear and flap retraction seemed normal. Enroute portion of the flight was normal.During the approach into ZZZZ; as flaps were extended; they came out normally to Flaps 1; but we heard a slightly unusual noise. As Flaps 5 were selected; a flaps EICAS appeared; followed very shortly afterwards by a Hyd EICAS message; C Hyd Press. At this point; the Captain as pilot monitoring (PM) selected the status page and we saw C Hyd quantity dropping through about 50% and dropped within a few seconds to zero.We broke off the approach and asked for a place to go to work the issue. We were given a climb and a hold at ZZZZ1. Once safely climbing and then established in Holding; the Captain and I referenced the QRH for C Hyd Press and the First Officer (FO) acted as pilot flying (PF). We elected to get the flaps out to 5 right away via the alternate system. We then reviewed the remainder of the checklist noting the need to extend flaps and gear via alternate system; and that; depending on the results of follow-on steps; may not have steering and require a tow to the gate. As Relief Pilot; I made the initial contact with the Flight Attendants (no Prep); the Captain coordinated with ATC for a long final and the possibility of stopping on the runway. ATC inquired about a [priority handling request] and the Captain confirmed that we were.We left holding and went to Flaps 20 shortly afterwards during vectors to intercept the ILS; then put the gear down at approximately 12 miles. It was clear below about 4000 and wind was calm. ATC did a great job with comfortable vectors and accommodating our requests. FO did a great approach and landing; stopping was not an issue. However; upon taking control of the aircraft and attempting to clear the runway; the Captain determined that steering was not available. We stopped on the runway for about 10-15 minutes while Crash Fire Rescue (CFR) looked over the airplane and we waited for the tow.Tow to the gate; parking; and termination were normal. However; we did wait a while for buses for the Passengers; and the Captain debrief with local maintenance and Police took some time.Overall; I thought it was a good real-world execution of how we are trained to handle non-normal situations. The Captain exercised overall command and authority; the FO did a great job as PF handling the aircraft; and as the Relief Pilot; I worked the checklist with the Captain (PM) and made inputs and assisted where able.