LOSS OF SEPARATION OCCURRED WITH A C750 EBOUND WITH ZOB AND A DC10 WBOUND WITH ZNY WITH INTERFAC COORD BREAKDOWN.

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I RELIEVED PREVIOUS CTLR. THE C750 WAS APCHING JST CLBING TO FL290 (WANTED FL410 FOR FINAL); DIRECT TO DQO. BECAUSE OF WBOUND TFC AT FL310 AND CLBING TO FL310 ON J80 E OF THS; I CALLED HARRISBURG SECTOR AND TOLD THEM THE C750 WAS STOPPED AT FL290. HARRISBURG SAID FL290 WAS APPROVED ON THE C750. THEN HARRISBURG CALLED BACK AND SAID TO CLB THE C750 TO FL330. I OBSERVED THE DC10 (WBOUND ON J80) WAS STILL SHOWING LEVEL AT FL290. I CLBED THE C750 TO FL330. I THEN OBSERVED THE DC10 CLBING. HARRISBURG CAME OVER THE 'SHOUT' LINE AND TOLD ME TO STOP THE C750 AT WHATEVER ALT HE WAS CURRENTLY AT. I STARTED TO DO THAT; BUT MY TRAINER USED HIS OVERRIDE AND KEPT C750 CLBING TO FL330. I STARTED TO TURN THE C750 N; BUT MY TRAINER SAW THAT HARRISBURG HAD TURNED THE DC10 N; SO HE OVERRODE ME AND TURNED THE C750 S. MY TRAINER CALLED TFC TO THE C750 WHO RPTED THAT IT HAD PASSED BEHIND HIM. WHEN THE C750 REACHED FL330; THE C750 WAS CLRED DIRECT DQO. SUPPLEMENTAL INFO FROM ACN 623435: THE C750 WAS APPROVED WITH ZNY AT FL290 (REQUESTED FL410). ZNY CALLED BACK TO HAVE US CLB THE C750 TO FL330. TRAINING AT ZNY WAS A FACTOR. ZNY CLBED THE DC10 FROM FL290 TO FL310; NOT KEEPING SEPARATION WITH THE C750. ZNY USED POOR JUDGEMENT IN HAVING US CLB THE C750 AND THEN CLBING THE DC10 TOO. ZNY NEEDED TO ISSUE TURNS TO DC10 TO BE CLR OF THE C750 BEFORE CLBING. WE TURNED THE C750 OUT TO THE S SO THEY WOULD NOT HIT. ZNY REFUSED TO TALK TO US TO COORD ANY TURNS ON TFC. ZNY HAS TO GET OUT OF THE HABIT OF CLBING ACFT ON THE BOUNDARY WITH ZOB. ZNY NEEDS TO INITIATE VECTORS SOONER SO THEY CAN CLB ACFT TO THEIR REQUESTED ALT SOONER. SUPPLEMENTAL INFO FROM ACN 622911: THE ACFT #1 WAS COORD WITH ZNY AT FL290. ACFT #2 WAS OPPOSITE DIRECTION AT FL290 SHOWING FL310. ZNY CALLED BACK AND INSTRUCTED THE RADAR CTLR TO CLB ACFT #1 TO FL330. AFTER CLBING; WE OBSERVED ACFT #2 CLBING OUT OF FL290. WE TURNED ACFT #1 TO A RADAR VECTOR 180 DEG HDG TO AVOID ACFT #2.