A B757-200 TAXIING WITH L ENG SHUT DOWN FOUND THAT THE NOSE GEAR WOULD NOT TURN R. HAD EICAS WARNING 'PWR TRANSFER UNIT.' MAINT RESET EICAS WITH BOTH ENGS RUNNING. SHUT DOWN L HYDRAULIC PUMPS FOR PWR TRANSFER TEST. BACK TO GATE WITH PWR TRANSFER SYSTEM INOP.

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UPON SINGLE ENG TAXI (R ENG RUNNING). TAXIED WITH INITIAL L TURN FOLLOWED BY AN ATTEMPT TO TURN SLIGHTLY R. NOSEWHEEL STEERING WOULD NOT TURN R. THIS WAS IMMEDIATELY FOLLOWED BY 'POWER TRANSFER UNIT' (PTU) ON LOWER EICAS SCREEN. CHKED L HYD PSI AND IT SHOWED 1100 PSI AND RECOVERING BACK TO NORMAL. CALLED MAINT VIA RADIO AND COULD NOT ELIMINATE EICAS MESSAGE 'POWER TRANSFER UNIT.' MAINT CAME OUT TO THE ACFT ON RAMP AND RESET EICAS MESSAGE WITH BOTH ENGS RUNNING. LIGHT WENT OUT. AGAIN RESTARTED TAXI TO RWY AND REQUESTED TO HOLD IN BLOCK WHILE WE POSITIVELY VERIFY THAT THE PTU WAS IN FACT OPERATING CORRECTLY. TURNED OFF BOTH L ENG DRIVEN AND ELECTRIC L HYD BOOST PUMPS AND AGAIN RECEIVED 'POWER TRANSFER UNIT' EICAS MESSAGE. NOW THE L HYD PSI WAS ZERO '0.' I HAD IN THE BACK OF MY MIND A FEW INSTANCES THIS PAST FEW WEEKS WITH HYD PROBS HAD WE HAD ONE OF THE PREVIOUSLY MENTIONED PROBS INFLT; WE MAY HAVE HAD A REAL PROB. INCIDENTALLY; THIS PROB WAS ADDITIONALLY ADDRESSED AT ZZZ1; HOWEVER NOT FIXED. SIMPLY AUTO CANCELING THE PROB DOES NOT FIX IT. WE RETURNED TO ZZZ GATE AS ACFT WAS OTS FOR REPLACEMENT OF PWR TRANSFER UNIT (PTU). CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: A RESET OF THE EICAS WARNING IS NO FIX AND THE RPTR SUSPECTED THE PWR TRANSFER UNIT WAS NOT OPERATING NORMALLY. THE L ENG WAS SHUT DOWN AND WITH THE R ENG RUNNING THE PWR TRANSFER SYSTEM FAILED TO POWER THE FLAPS; SLATS; LNDG GEAR; AND NOSE STEERING.