SMA X HAD CONFLICT WITH HELI Y WHILE TAXIING TO RWY. SEE AND AVOID CONCEPT.

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I WAS WORKING FLT DIRECTOR; GND CTL; CLRNC DELIVERY AT EYW. I TAXIED SMA X PA28 VFR TO RWY 9. AS X WAS TAXIING WBOUND ON THE PARALLEL TXWY; I OBSERVED Y HELI INBOUND FROM SW. I ISSUED X THE HELI TFC FROM SW; AND; SINCE I HAD NOT RECEIVED COORD FROM LCL; I TOLD X TO CONTINUE TAXIING AND THAT HELI WOULD PASS BEHIND HIM. PER 7110.65 IN HELI OPS; HELI'S ARE SUPPOSED TO REMAIN CLR OF ALL FIXED WINGED ACFT; AND SINCE I WAS WORKING GND CTL; THE TXWY BELONGED TO ME. AFTER ADVISING X ABOUT THE HELI; I OBSERVED Y TAXIING EBOUND ON MY TXWY (OPPOSITE DIRECTION TO X) WITHOUT HAVING RECEIVED COORD APPROVAL FROM ME. Y THEN TURNED SLIGHTLY S AND PROCEEDED TO PARK ON THE DIAGONAL TXWY. X STOPPED TAXIING AND THEN CONTINUED TO TAXI WBOUND WHEN Y MOVED. NO FURTHER INCIDENT OCCURRED. HOWEVER; AFTER THIS SIT; LCL CTLR BECAME UPSET AND TOLD ME HE HAD COORDINATED THE OP AND HAD RECEIVED APPROVAL. I TOLD HIM THAT I DID NOT HEAR HIM COORDINATE THIS OP; AND THAT IF I HAD HEARD AND APPROVED THE COORD; I WOULD NEVER HAVE ISSUED X TAXI INSTRUCTIONS AND INFORMED X THAT Y WOULD PASS BEHIND HIM.