NMAC BETWEEN CORP JET AND UNKNOWN SMALL ACFT.

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WE WERE BEING VECTORED FROM METRO INTXN TO THE VOR B APCH AT TEB. WE WERE CLRED TO DSND FROM 8000' TO 3000'. DSNDING THROUGH 5000' WE WERE GIVEN 'STOP DSCNT AT 4500' TURN L HDG 300 DEG FOR TFC.' MY COPLT RESET THE ALT SEL TO 4500'; I VERIFIED ALT ARM/CAPTURE AND ROLLED THE HDG BUG TO 300 DEG. AS THE ACFT LEVELED AT 4500' I ADDED PWR AND LOOKED INSIDE TO VERIFY N; WHEN I LOOKED UP AGAIN SMALL ACFT Y WAS VIRTUALLY MOTIONLESS IN MY WINDSHIELD AT OUR ALT. AS MY ACFT WAS STARTING TO ROLL OUT OF THE TURN I ROLLED BACK INTO A 035 DEG TO 040 DEG L BANK AND TURNED 15 TO 20 DEGS BY THE ASSIGNED HDG. ACFT Y PASSED OFF OUR R SIDE WITH NOT MORE THAN 100' LATERAL SEP. AS I RECALL THE CTLR ISSUED 'TFC IN YOUR TURN AT 12 O'CLOCK' AT THE SAME TIME I SAW ACFT Y. I WISH THE TFC WOULD HAVE BEEN ISSUED BEFORE THE TURN. HAD I SEEN THE TFC EARLIER I COULD HAVE BEEN PART OF THE DECISION PROCESS RATHER THAN JUST REACTING TO A CTLR CREATED SITUATION. ANY SOLUTION; OTHER THAN TURNING AT THE TARGET; WOULD HAVE BEEN SAFER. CALLBACK CONVERSATION WITH RPTR REVEALED FOLLOWING INFO. THERE WAS NO REVIEW WITH ATC AFTER LNDG; AND RPTR FLT CREW DID NOT FILE NMAC RPT WITH FAA. SAYS ACFT Y WAS STILL OUTSIDE OF TCA AND CTLR WAS FOLLOWING TARGET TO SEE IF TCA WAS PENETRATED. ACFT Y WAS UNKNOWN VFR TFC. ACFT X NBOUND AND Y WAS NEBND. X PASSED SLIGHTLY BEHIND Y AFTER EVASIVE MANEUVER.