DURING A VERY BUSY TIME AT SJC ARPT; THE GND MAY HAVE LOST TRACK OF ACFT TAXIING TO THE RWY RESULTING IN MISIDENT OF WHO WAS THE #1 ACFT TO TAKE OFF.

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WE CALLED SJC GND FOR PUSH CLRNC AT APPROX XA03L AND WERE TOLD TO HOLD AT THE GATE; SJC GND WAS VERY BUSY WORKING MULTIPLE ACFT AND THE CTLR SOUNDED TASK SATURATED. AT XA10L WE CALLED AGAIN FOR OUR PUSH CLRNC AS WE DID NOT SEE ANY REASON TO BE HOLDING AT THE GATE. SJC GND CLRED US TO PUSH WHEN COMPANY WAS CLR BEHIND US AND TOLD US WE DID NOT HAVE CLRNC TO LAX. WE TOLD SJC GND WE DID HAVE OUR CLRNC AND HE TOLD US THERE WERE FLOWS TO LAX AND HE WOULD GET US A FLOW TIME. I TOLD THE PUSHBACK DRIVER WE WERE CLRED TO PUSH WHEN COMPANY WAS CLR BEHIND US AND HE TOLD ME THERE WERE NO ACFT BEHIND US AND WE STARTED TO PUSH FROM THE GATE. SHORTLY AFTER WE STARTED TO PUSH; FLT ABC RECEIVED PUSH CLRNC FROM ANOTHER GATE. ALL DURING THIS TIME; SJC GND WAS CONFUSING MANY OF OUR COMPANY FLT NUMBERS WHEN RESPONDING TO US AS 4 OF US WERE TRYING TO PUSH AT THE SAME TIME AND SEVERAL COMPANY ACFT WERE HOLDING OUT FOR GATES. WE WERE READY TO TAXI BEFORE ABC; BUT WAITED TO CALL FOR TAXI CLRNC UNTIL ABC WAS CLRED TO TAXI. OUR CLRNC WAS TO FOLLOW COMPANY TO RWY 30 VIA TXWY ZH -- TXWY Y TO RWY 30 WITH A WHEELS-UP TIME OF 1925L TO LAX; WHICH WE ACKNOWLEDGED. AS WE CLOSELY FOLLOWED AND MADE THE TURN ONTO TXWY H; MY FO LOOKED R TO CLR TXWY Y FROM THE NW AND DIRECTED ME TO STOP! ACFT Y (B757 ACFT) TAXIED PAST US ON TXWY Y. SJC GND DID NOT INFORM US OF ANY POTENTIAL CONFLICT AT TXWY H-Y NOR DID THEY DIRECT ACFT Y FLT TO FOLLOW EITHER OR BOTH COMPANY ACFT. ONCE ON TXWY Y BEHIND ACFT Y; WE CALLED SJC GND AND ADVISED THEM THAT WE WERE FOLLOWING ACFT Y TO RWY 30. SJC GND WAS STILL VERY BUSY AND DID NOT ACKNOWLEDGE OUR RADIO CALL. AS WE APCHED TXWY B ON Y; ABC WAS CLRED INTO POS AND HOLD ON RWY 30. WE ADVISED TWR THAT WE WERE BEHIND ACFT Y. SJC TWR WAS BUSY AND DID NOT RESPOND TO OUR RADIO CALL. AFTER ABC WAS CLRED FOR TKOF; SJC TWR CLRED US TO TAXI INTO POS AND HOLD (THE TIME WAS XA24L). I TOLD MY FO TO ADVISE SJC TWR THAT WE WERE TAXIING INTO POS AND HOLD FROM TXWY B1; WHICH HE DID. SJC TWR DID NOT RESPOND. I TURNED MY LNDG LIGHTS ON AND WE BEGAN OUR TAXI INTO POS AND HOLD FROM TXWY B1 WHEN SJC TWR ASKED US IF WE WERE BEHIND ABC. WE RESPONDED 'AFFIRMATIVE' AND THEN SJC TWR SAID WE ARE NOT SUPPOSED TO TAXI INTO POS AND HOLD FROM B1; BUT SINCE YOU'RE ALREADY DOING IT; TO CONTINUE. SHORTLY THEREAFTER; WE WERE CLRED FOR TKOF. I AM PROVIDING THIS INFO BECAUSE OF THE POTENTIALLY DANGEROUS SIT WE WITNESSED. SJC GND WAS EXTREMELY BUSY -- APPEARED TO BE BEYOND TASK SATURATION AND HAD LITTLE IF ANY IDEA WHO WAS WHO ON THE GND OR WHERE THEY WERE GOING. 1 RADIO CALL FROM SJC GND TO US OR TO ACFT Y COULD HAVE RESOLVED THE POTENTIAL CONFLICT AT TXWY H-Y. SECONDLY; BECAUSE SJC GND WAS OUT OF THE LOOP ON TFC FLOW; SAN JOSE; CA TWR WAS UNAWARE THAT WE WERE BEHIND AMERICAN AT THE APCH END OF RWY 30. THIRDLY; NEITHER SJC GND NOR TWR ACKNOWLEDGED EITHER ONE OF OUR RADIO CALLS ADVISING THEM THAT WE WERE FOLLOWING ACFT Y. (AT THE TIME BOTH CTLRS WERE BUSY; BUT NEITHER CTLR UNDERSTOOD WHAT WE WERE TELLING THEM BECAUSE OF THEIR HVY WORKLOAD.