AN SMA PLT HAD TROUBLE ENTERING NQX AIRSPACE.

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AT ABOUT XA30; I AND 2 PAX (BOTH PLTS) DEPARTED VFR FOR CUDJOE KEY EYW DEP INSTRUCTED A R TURN FROM RWY 9 AND TURNED US OVER TO DEP ON 199.25. DEP; WHICH IS ACTUALLY AT NQX; GAVE US A SQUAWK CODE ND INSTRUCTIONS TO 'REMAIN 1 MI OFFSHORE AND AT OR BELOW 1000 FT.' WE COMPLIED AND WERE RELEASED FROM RADAR ADVISORIES AS WE APCHED CUDJOE KEY. WE SPENT ABOUT 45 MINS AT CUDJOE PHOTOGRAPHING AND STARTED TO RETURN TO KEY WEST; REMAINING AT LEAST 1 MI OFFSHORE AND AT 800 FT AGL. BEGAN CALLING KEY WEST APCH ON 199.25 AT ABOUT SUGARLOAF KEY. CTLR WAS BUSY HANDLING BOTH MIL AND CIVILIAN TFC. CONTINUED CALLING AND DID A COUPLE OF 360 DEG TO KEEP CLR OF NQX AIRSPACE. FINALLY CONTACTED CTLR AND TOLD HIM I WAS SE OF NQX; LNDG EYW. THE REPLY WAS 'REMAIN VFR.' NO SQUAWK; NO VECTORS; NO OTHER INSTRUCTIONS; NOTHING. A COUPLE OF MINS LATER; HE GAVE ME INSTRUCTIONS TO 'TURN 180 DEG' AND I COMPLIED. WHEN I WAS ABOUT 5-6 MI OFFSHORE; THE CTLR (I ASSUME THE SAME ONE) ASKED WHY I WAS THERE. I TOLD HIM THAT ABOUT 45 MIN AGO I PASSED THERE ON THE WAY TO CUDJOE AND THESE WERE MY INSTRUCTIONS. ANOTHER CTLR CAME ON THE RADIO AND SAID 'I WAS WORKING THEN AND GAVE NO SUCH INSTRUCTIONS TO ANYONE.' THIS WAS NOT TRUE. ASKED FOR MY NAME AND I GAVE IT TO HIM. HE THEN GAVE ME THE INSTRUCTION 'FREQ CHANGE APPROVED;' AND HE WAS GONE. I CALLED EYW TWR AND RPTED ABOUT 6 SE LNDG EYW. I WAS TOLD TO ENTER R DOWNWIND AND I WAS CLRED TO LAND. ON THE GND; I TALKED TO AN INSTRUCTOR AT AN FBO AND SHE CALLED NQX APCH AND TALKED TO SOMEONE. SHE LATER SAID THAT THEY HAVE HAD THE SAME PROBS WITH SOME NQX CTLRS. THEY ARE VERY YOUNG; NOT REALLY EXPERIENCED; MOST ARE NOT PLTS; ETC. IN THIS SIT; I BELIEVE THIS CTLR WAS HANDLING MORE TFC THAN HE WAS CAPABLE OF HANDLING. HE SOUNDED EXTREMELY FRUSTRATED AND AGITATED. FOR EXAMPLE; ON MY INITIAL CONTACT; I WAS TOLD TO 'REMAIN VFR.' WHAT DOES THIS MEAN? THE ONLY WAY I COULD HAVE DONE OTHERWISE WOULD HAVE BEEN TO HAVE CRASHED INTO THE OCEAN.