MD88 FLT CREW EXPERIENCED CONFLICT WITH PRECEDING ACFT DURING VISUAL APCH TO LGA.

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ESTABLISHED ON VISUAL TO RWY 31 AT LGA WHEN TWR CALLED TFC TO FOLLOW AT 12 O'CLOCK POS. THE CAPT AND I SAW AN ACFT AT APPROX 12 O'CLOCK POS; TURNING AROUND SHEA STADIUM ON 1-2 MI FINAL. WE WERE 2 MI INBOUND FROM POINT 'DIALS' (ABOUT 4 MI FROM LNDG). WE WERE FOLLOWING ACR Y TO FINAL. WHEN 1 1/2 MI FROM TOUCHDOWN (CIRCLING AROUND SHEA STADIUM OURSELVES); THE TCASII RA CALLED 'TFC' AS TWR DIRECTED A HARD R TURN. I SAW AN ACFT APPROX 500 FT AWAY AT CO-ALT ALSO TRACKING INBOUND TO RWY 31. WE EXECUTED THE AVOIDANCE MANEUVER AND REJOINED FINAL. TWR LATER TOLD US THAT THE ACFT WE BARELY AVOIDED ACR Z; HAD BEEN PRECEDING US ON THE EXPRESSWAY VISUAL BUT HAD 'EXTENDED THEIR FINAL' BY SOME MANEUVER THAT RESULTED IN THEM REJOINING THE PUBLISHED MANEUVER AT THE SAME PLACE AND TIME AS US. WE WERE CLRED FOR AND ESTABLISHED ON THE PUBLISHED VISUAL APCH PROC AND NOTIFIED TO FOLLOW TFC 3 MI AHEAD. THIS MADE SENSE. WHEN ACR Z SHOWED UP OUT OF NO WHERE; TWR INDICATED THAT WE WERE SUPPOSED TO FOLLOW HIM! SINCE HE HAD DEVIATED FROM THE PUBLISHED MANEUVER (AND WAS OFF SOMEWHERE GETTING SPACING); WE DID NOT SEE HIM. IF WE WERE 4 MI OUT; HOW COULD TWR HAVE 1 ACFT AT 1 MI OUT AND WE BE #3 FOR LNDG? TWR LOST SITUATIONAL AWARENESS ON ACR Z AND DID NOT NOTIFY US OF HIS POS OR THAT HE WAS REJOINING THE VISUAL GND TRACK. A NEAR MIDAIR WAS THE RESULT.