DURING CLBOUT FROM TPA THROUGH 10500 FT; AN A320 CREW RECEIVE A TCASII RA AND TAKE EVASIVE ACTION; THEN SPOT A KING AIR ACFT XING OVER THE TOP.

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HANDOVER FROM TPA APCH TO ZJX PASSING 10000 FT; JAX ROGERED OUR HANDOVER AND CLRED US TO CLB TO FL230. PASSING 10500 FT GOT A TCASII TA FOR TFC AT 12000 FT 3 TO 4 NM AT 1 O'CLOCK POS. AT 11000 FT GOT A TCASII RA DIRECTING US TO ADJUST VERT SPD TO ZERO. I ADJUSTED AND SAW TFC VISUALLY; COPLT ADVISED JAX OF OUR RA. AFTER CLR OF CONFLICT; WE INQUIRED IF JAX HAD ANY WARNINGS OR AWARENESS OF CONFLICT TFC. RESPONSE WAS SOMETHING LIKE; 'YOU STARTED TO FLASH JUST AS YOU CALLED ME ON IT' AND 'TFC (KIND AIR) IS VFR.' I AM TROUBLED THAT WITHOUT TCASII AND VFR CONDITIONS THIS COULD HAVE BEEN A MISHAP; AND JUDGING BY OUR FLT PATHS PROBABLY WOULD HAVE BEEN. SUPPLEMENTAL INFO FROM ACN 640035: THE TCASII RPTED HIS ALT PLUS 1000 FT ONCE WE LEVELED OFF AT 11000 FT AND HE PASSED DIRECTLY OVER TOP OF US. THE JAX CTLR WAS VERY BUSY DURING THIS TIME AND WAS DIRECTING OTHER ACFT NON-STOP AND WE COULD NOT BREAK INTO THE RADIO UNTIL AT LEAST 1-2 MINS AFTER THE EVENT OCCURRED. ONCE WE RPTED THE RA TO THE CTLR; HIS RESPONSE WAS THAT THE KING AIR WAS VFR. I RESPONDED THAT WE WERE IFR. THE CTLR THEN GAVE US PHONE TO CALL AND TALK ABOUT THE SIT. I DID CALL BEFORE I MADE THIS RPT AND JAX WAS VERY HELPFUL AND CONCERNED ABOUT THE INCIDENT. THEY MARKED THE REPLAYS AND ARE FORWARDING THIS TO THEIR QUALITY ASSURANCE. THEY RPTED THAT THIS HAPPENED IN THEIR SECTOR 14.