XFERRING ARTCC RADAR CTLR FAILS TO ISSUE PLANNED CTL INSTRUCTIONS TO DSNDING ACR AND XFERS ACFT TO NEXT CTL SECTOR. XFERRING CTLR COORD WITH NEXT SECTOR PLANNED CTL ACTIONS. RECEIVING CTLR INITIATES ACTIONS TO SEPARATE ACFT WHEN OEDP ACTIVATES; BUT ACTIONS ARE NOT SUFFICIENT TO MAINTAIN SEPARATION.

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ACFT #1 WAS HEADING N. I WAS INFORMED BY PREVIOUS CTLR IT WAS TO INTERCEPT ON AIRWAY 10 MI S OF ACFT #2; WHICH WAS CLBING WESTERLY. HOWEVER; ACFT #1 WAS NOT TOLD TO JOIN THE AIRWAY; BLEW THROUGH IT ON DSCNT; AND CAME INTO CONFLICTION WITH ACFT #2. THE PREVIOUS CTLR HAD MISINFORMED ME. I ATTEMPTED TO ESTABLISH VERT SEPARATION. I MANAGED TO STOP THE 2 ACFT CLB/DSCNT AND PREVENTED COLLISION; BUT NOT IN TIME TO PREVENT LOSS OF SEPARATION. THIS WAS A CASE OF HUMAN ERROR ON THE PART OF THE PREVIOUS CTLR. SUPPLEMENTAL INFO FROM ACN 410816: ACR #1 INBOUND TO DTW FROM TPA; CHKED ON MY FREQ AT FL290. ACR #1 WAS TURNED 15 DEG VECTORS FOR THE CETUS 2 ARR. MY ATTN SHIFTED TO OTHER ACFT. MY INTENTION WAS TO GIVE ACR #1 A HEADING TO JOIN THE CETUS 2 ARR WHICH WAS COORDINATED WITH THE NEXT CTLR. AFTER FINISHING UP SOME OTHER STUFF; ACR #1 WAS DSNDED TO FL240; SPD 300 KTS OR GREATER; BUT I DIDN'T ISSUE THE HEADING TO JOIN. I SWITCHED ACR #1 TO THE NEXT SECTOR WHERE THE OEPD ACTIVATED IN THE DSCNT TO 12000 FT WITH ANOTHER ACFT IN THE OTHER SECTOR.