POTENTIAL CONFLICT BETWEEN ACR-LGT AND UNAUTH GA-SMA IN TCA.

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UNDER LGA APCH CTL ON DOWNWIND FOR VOR C APCH TO RWY 22 LGA AT 3000'; HDG 050 DEGS. TFC WAS GIVEN AT 12 O'CLOCK; 3 MI (APCH WAS NOT TALKING TO HIM). IMMEDIATELY AFTER THAT XMISSION WE WERE GIVEN A TURN TO 260 DEGS AND DSCNT TO 2000' I THOUGHT THIS WOULD TURN US INSIDE THE TFC WHICH WAS SBND. IN THE TURN THE FE SPOTTED TFC AT 10 O'CLOCK; 1 1/2-2 MI; WHICH APPEARED TO BE AT 2500-3000'. I STOPPED THE TURN TO GO BEHIND THE TFC WHICH THEN APPEARED TO BE DSNDING THROUGH OUR ALT. I ESTIMATE THAT WE PASSED APPROX 1000' BEHIND SMA; WHICH WAS DSNDING (HE WAS RIGHT ON THE VOR C R FOR RWY 22). WE OVERSHOT THE INBND RADIAL TO THE W AND WENT AROUND THE TFC AND REINTERCEPTED THE RADIAL AND CONTINUED TO A NORMAL LNDG. I DIDN'T GET EXACT MILEAGES; BUT I BELIEVE THE SMA WAS APPROX 12 NM FROM LGA WHEN WE SPOTTED HIM AT 2500-3000'; 10 NM AS WE PASSED HIM (HE WAS THEN ABOUT 2000') AND ABOUT 6-7 NM WHEN WE WERE ESTABLISHED BACK ON THE RADIAL. ONCE ON THE GND I CALLED APCH TO FIND OUT IF THEY KNEW ANYTHING MORE ABOUT THE TFC. THEY SAID THEY TRIED TO TRACK HIM BUT HE DROPPED OFF THE RADAR. THIS IS ANOTHER CASE OF A LIGHT ACFT WHERE HE DIDN'T BELONG; THAT IS IN THE TCA OF A VERY BUSY ARPT.