REROUTING OF TFC BY ZOB AND WX DEVS MAY HAVE CAUSED A LOSS OF SEPARATION BY A RADAR CTLR.

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WE HAD BEEN REROUTING EWR ARRS INTO THE JFK AND SATELLITE ARR STREAM FOR APPROX 20-30 MINS WHEN NEW YORK JFK SECTOR SHUT US OFF. WHEN THIS OCCURS; AN ALREADY COMPLEX SECTOR BECOMES FAR MORE COMPLEX. DISCUSSIONS IMMEDIATELY START CONCERNING WHO WE HAVE TO HOLD; WHERE WILL WE HOLD; WHO WE WILL HAVE TO SHUT OFF IN ADDITION TO STAYING ABREAST OF TFC SITS. ACR X (B767) WAS AT FL390 AND REQUESTING A W (L) DEV FOR WX. KNOWING THIS WOULD PUT HIM IN CONFLICT WITH AN AIRPLANE AT FL390 OVER JHW; I DSNDED HIM. I HAD OVERLOOKED ACR Y (B757) WHO WAS TURNING AROUND BECAUSE JFK WOULD NOT TAKE HIM. IN SITS SUCH AS THIS; THE CONFLICT ALERT IS USELESS. BY THE TIME I REALIZED THE CONFLICTION; I TRIED TO STOP ACR X'S DSCNT; BUT INADVERTENTLY CALLED HIM ACR Z. I DSNDED ACR Y AND HE ACKNOWLEDGED AND STARTED DOWN. THE 2 PLANES WERE ON A POTENTIAL COLLISION COURSE. JUST AS ACR Y STARTED DOWN; ACR X ADVISED RESPONDING TO TCASII AND CLBED FROM FL376 UP TO FL379. ACR Y SAID HE TOO HAD A TCASII ALERT. IF I HAD NOT HAD A LAPSE IN AWARENESS; THE SYS ERROR WOULDN'T HAVE OCCURRED. HOWEVER; IF ACR Y HADN'T BEEN REROUTED OR SPUN OUT; THIS WOULDN'T HAVE OCCURRED.