MIL FGT'S CLB THROUGH OCCUPIED ALT HAD LTSS FROM ACR X. SYS ERROR.

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I WAS WORKING ACR X ON A 110 DEG VECTOR TO JOIN MZB 320 DEG RADIAL (STANDARD HDOF) WHEN ANOTHER SECTOR ATTEMPTED TO HDOF A FLT OF 2 FGT'S DEPARTING SBOUND TO A WARNING AREA OFF SHORE. I HAD ACCEPTED THE HDOF (CLBING TO 7000 FT) AND ALREADY HANDED THE FGT'S OFF TO THE NEXT SECTOR WHEN THE TRANSFERRING CTLR CALLED ME TO ASK MY UHF FREQ. I TOLD HIM TO JUST GIVE HIM TO THE NEXT SECTOR SINCE THEY ALREADY ACCEPTED THE HDOF. HE SAID 'THEY'LL BE CLBING TO 12000 FT' AND I AGREED; ASSUMING THE FGT'S WOULD CONTINUE THEIR CLB RATE AND BE WELL ABOVE MY ACR X. THEY DIDN'T. I TRIED TO GET THE SECTOR WORKING THE FGT'S TO LEVEL THEM AT 80 BEFORE IT BECAME A LOSS OF SEPARATION; BUT THE FGT'S WERE UNABLE TO LEVEL IN TIME. I SHOULD HAVE TAKEN THE FGT'S AND STOPPED THEM AT 80 AND UNTIL I WAS SURE THERE WASN'T A CONFLICT. JUST BECAUSE THE OTHER SECTOR HAD TAKEN THE HDOF; I SHOULDN'T HAVE TAKEN A POINTOUT WITHOUT ISSUING CONFLICTING TFC. AT THE SAME TIME; ANOTHER SECTOR TRANSFERRED COMS ON ANOTHER ACFT TO ME WITHOUT A HDOF; SO I WAS DISTRACTED WHILE I ATTEMPTED TO FIND OUT WHO WAS CALLING ME.