MD-11 First Officer reported failure of both tail fuel pumps. Subsequently; the #2 engine showed zero fuel flow and began to roll back. The flight crew requested priority handling and performed an air turn back and precautionary landing at departure airport.

Narrative

Approximately around XA:20z climbing though FL380 for FL400; we got a level two alert for Tail Fuel Pumps LO. At this time the PF was told to continue flying and the PIC and Relief Pilot; will conduct the Quick Reference Hand book; abnormal procedures fuel 'Tail Pumps Lo' procedure. We conducted the procedure getting to the turn on tail tank alt pump switch 'on'; it was only green for about 30 seconds and went amber. There was 1;450 kilograms of fuel in tail tank and we had another alert 'Alt Tail Pump Lo'. At this point the aircraft is leveling off at FL400. The fuel flow looked normal for all three engines but when the power was moving back for cruse setting the number 2 engine just continued to roll back to flight ideal with 0 fuel flow. At this point the PIC asked ATC for FL340 to work of fuel issue. The procedure was completed by this point and the PIC asked crew if they would like to attempt a restart or just return to ZZZZ. PIC agreed with crew to return due to the close distance to ZZZZ and the ability to have any services need at this location. The PIC asked for the Engine shutdown in flight Procedure. Once completed the PIC loaded the ZZZZ ILS XXL approach in the flight computer. The PF briefed the approach and the aircraft landed with no further issues.