ATC CONFUSION REIGNED WHEN AN ACR B737-300 HAD TRIALS AND TRIBULATIONS WITHIN THE TFC PATTERN FOR A NIGHT VISUAL APCH TO OAK; CA.

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ATC CONFUSION. WE WERE SENT AROUND FROM SHORT FINAL TO RWY 29 BECAUSE A LNDG ACFT DID NOT CLR THE RWY IN TIME WITH ANOTHER ACFT CLRED 'INTO POS AND HOLD.' THE TWR GAVE US THE OPTION TO TURN DOWNWIND (L) AT 1500 FT AND TO STAY WITH HIM; WHICH WE ACCEPTED. WE WERE THEN TOLD TO TURN BASE BEHIND 'COMPANY Y' AT OUR 9 O'CLOCK POS. AS WE BEGAN OUR TURN; WE WERE BROKEN OFF THE APCH AND TOLD TO FOLLOW ANOTHER ACFT (ACFT Z) NOW AT OUR 11 O'CLOCK POS. THERE WAS CONFUSION BTWN TWR AND ACFT Z AS TO THE CLRNC ACFT Z WAS GIVEN. WE CONTINUED OUR DOWNWIND AND AGAIN WERE TOLD TO FOLLOW ACR Z NOW AT OUR 9 O'CLOCK POS. ACR Z WAS NOW BEHIND THE COMPANY Y ACFT THAT WE WERE ORIGINALLY TOLD TO FOLLOW. AS WE MADE OUR TURN TO BASE; WE RECEIVED AN URGENT CALL ASKING US IF WE HAD OUR OTHER COMPANY XX IN SIGHT AT 12 O'CLOCK POS. WE LOOKED AND ACQUIRED THE TFC THEN IMMEDIATELY MADE A R TURN BACK TO A DOWNWIND HDG. AS WE PASSED THE TFC; WE DID RECEIVE A TCASII TA. WE FINALLY TURNED BASE AND ACCOMPLISHED THE APCH ON OUR THIRD ATTEMPT. APPARENTLY; THE TWR HAD FORGOTTEN THAT THERE WAS A COMPANY ACFT ALREADY FOLLOWING ACR Z WHEN WE WERE TOLD TO DO THE SAME. IN A SUBSEQUENT TELEPHONE CONVERSATION WITH THE TWR; THEY INDICATED TO ME THAT THEY FELT WE HAD DONE NOTHING WRONG; AND THAT THE CONFUSION WAS BTWN THEM AND SOME OTHER ACFT. THEY ALSO MENTIONED THAT AT TIMES THEY RECEIVE VERY SHORT NOTICE AS TO THE EXACT NUMBERS AND SPACING OF ACFT INBOUND FROM APCH CTL. THE EVENT AND AN ALMOST IDENTICAL EVENT IN THE MIL YRS AGO LED ME TO THE CONCLUSION THAT IT IS VERY DIFFICULT FOR TWR CTLRS TO INTEGRATE A SUDDEN VFR PATTERN INTO THEIR IFR ARRS. IF GIVEN THE OPTION; THE BEST COURSE OF ACTION FOLLOWING A GAR SEEMS TO BE A RETURN TO APCH CTL.