FLC OF AN LGT TURNED AND LEVELED OFF IN RESPONSE TO A TCASII RA.

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APCHING RBV ON CLBOUT OF JFK; PASSING APPROX 14000 FT; CLRED TO 17000 FT. RECEIVED TCASII TA FOR TFC AT 12 O'CLOCK; PLUS 1500 FT; CONVERGING WITH US. WE MADE A R TURN AND LEVELED AT APPROX 15000 FT; AND ASKED ATC ABOUT TFC. HE SAID SOMETHING ABOUT 'THAT'S WHY I LEVELED (SOMEBODY) AT (SOME ALT).' HE WAS GARBLED AND WHAT HE SAID DID NOT MAKE SENSE TO US. WE HAD NOT HEARD ANYBODY CALL ANY TFC OR TELL ANYONE TO LEVEL OFF. WE WERE STILL LEVELED AT APPROX 15000 FT AND TFC PASSED OFF TO OUR L AT ABOUT PLUS 600 FT AND 1000 FT AWAY. WE COULD CLRLY SEE IT WAS A TWIN TURBOPROP COMMUTER. THE CTLR THEN HANDED US OFF TO NEW CTLR. WE CHKED IN AND SHE IMMEDIATELY QUERIED US AS TO OUR ASSIGNED ALT. NONE OF US HAD HEARD ANYTHING DIFFERENT THAN 17000 FT SO THAT'S WHAT WE SAID. SHE SAID; 'ROGER; HIGHER IN 5 MI.' THIS APPEARED TO CONFIRM THAT WE HAD NOT BEEN ASSIGNED A LOWER ALT; WHICH THE PREVIOUS CTLR HAD IMPLIED. WE BELIEVE THE FIRST CTLR ERRED. THERE WAS A DEFINITE CONFLICT WHICH WAS RESOLVED (THANKFULLY) BY TCASII. NONE OF US HEARD A TFC CALLOUT OR AN ASSIGNMENT TO LEVEL OFF TO AVOID THE CONFLICT. AND IF THE CTLR DID ISSUE IT; WE DID NOT READ IT BACK; AND WITH SUCH A SERIOUS CONFLICT; YOU WOULD THINK THE CTLR WOULD DEFINITELY BE REQUIRING A READBACK OR SOME OTHER CONFIRMATION FROM US TO ACKNOWLEDGE THE CONFLICT.