B737 FLC TAKE EVASIVE MANEUVER DUE TO ZMA CTLR CHALLENGE AS TO WHERE THEY ACTUALLY ARE IN REF TO ANOTHER ACFT WITH THE SAME XPONDER CODE BELIEVED TO BE IN THE SAME PROX.

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FILED OVER MAXIM FL370 PROCEEDING TO KEY WEST FOR DUVAL ARR. CAPT'S LEG; FO ON THE RADIO. ATC FREQ 132.2 VERY BUSY -- CTLR BEING STEPPED ON AND TELLING EVERYONE TRYING TO CHK IN TO STAND BY. PREVIOUSLY ASSIGNED XPONDER CODE XXXX BY HAVANA FOR MIA. ABOUT 30-40 MI; 3-4 MINS PAST MAXIM (FIR) BREAK IN RADIO TFC ALLOWED US TO CHK IN AT FL370. CTLR SAID WE WERE ASSIGNED FL390. WE ASKED IF HE WANTED US TO CLB TO FL390; AND HE THEN GAVE US AN IMMEDIATE DSCNT FOR TFC CONFLICT LESS THAN 1 MI; 12 O'CLOCK POS; FL370. ALL OF THESE XMISSIONS INCLUDED OUR CORRECT CALL SIGN FROM BOTH WE AND THE CTLR. THIS WAS NOT A READBACK/HEARBACK TYPE ERROR. WE ACKNOWLEDGED AND INITIATED AN IMMEDIATE DSCNT (APPROXIMATING A TCASII TYPE MANUAL ESCAPE); THEN QUERIED THE CTLR FOR WHAT ALT I WAS TO DSND TO. I DID NOT RECEIVE AN IMMEDIATE REPLY AND ASKED AGAIN WHAT ALT HE NEEDED US AT. THIS WHOLE TIME I AM NOT CONVINCED THIS MANEUVER WAS NECESSARY BECAUSE THERE ARE NO TARGETS ON MY TCASII AT ANY ALT WITHIN ABOUT 20 MI (TCASII WAS SET TO BELOW FOR ARR); BUT THE CTLR WAS EMPHATIC AND SOUNDED VERY CONCERNED IN HIS INITIAL XMISSION. HIS NEXT XMISSION WAS ASKING AGAIN OUR CURRENT ALT; SO I IMMEDIATELY LEVELED OFF AT APPROX FL364; SUSPECTING THAT HE WAS NOT LOOKING AT ME AND NOW CONCERNED THAT HE HAD GIVEN ME A DSCNT WHILE LOOKING AT ANOTHER ACFT. ANOTHER PAUSE AND CTLR ASKED US TO IDENT; FOLLOWED BY CTLR COMMENT THAT HE DID NOT PREVIOUSLY 'HAVE' US; ALSO THAT HAVANA HAD GIVEN US A XPONDER CODE IDENTICAL TO ANOTHER ACFT HE WAS CTLING HE SAID; AND THAT THE ATC COMPUTER HAD NOT PICKED UP THE PROB. HE THEN GAVE US A CONTINUED DSCNT FOR A NORMAL ARR INTO MIA. I DO NOT BELIEVE; AND THERE WAS NO RPT; THAT ANY TFC CONFLICT OR LOSS OF SEPARATION EVER ACTUALLY OCCURRED WITH MY ACFT OR THE ACFT WITH THE SAME XPONDER CODE. I SUSPECT THAT THE CTLR WAS LOOKING AT THE OTHER ACFT THAT HAD THE SAME XPONDER CODE; AND WAS ACTUALLY LEVEL AT FL390; CONFUSING THE CTLR. I CONFIRMED THIS WITH A CALL TO THE ZMA SUPVR ON DUTY. THERE ARE NO ENTRIES IN THE ARTCC INCIDENT LOGBOOK CONCERNING THIS EVENT. THE ARTCC MGR SAID HE WOULD CHK INTO IT.