ARTCC MFD RADAR CTLR ACCEPTS HDOF ON A B737 FROM BSV CTL SECTOR CLBING; RESTR TO FL260. HOP CTLR ATTEMPTS TO POINT OUT AN DA10 DSNDING TO MFD CTLR. MFD CTLR INSTRUCTS THE BSV CTLR TO CONTINUE CLB TO REQUESTED FINAL ALT AND XFER COM. ALSO; THE MFD CTLR DECLINES A POINT OUT OF THE DA10; TAKES A HDOF AND CTL OF THE DSNDING DA10 FROM THE HOP CTLR; AND BECOMES DISTRACTED. WHEN THE CONFLICTION MATERIALIZES; THE MFD CTLR ATTEMPTS TO MAINTAIN SEPARATION; BUT IS UNABLE.

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BSV CTLR POINTED OUT ACFT #1 TO MFD RADAR CTLR. MFD CTLR TOOK RADAR ON ACFT #1 AND WAS PUT ON THE MFD FREQ. HOP WAS FLASHING THE HDOF ON ACFT #2 LNDG OSU. I ASKED HOP FOR CTL FOR LOWER ALT ON ACFT #2. SUPPLEMENTAL INFO FROM ACN 411841: AN DA10 FROM ERI TO OSU AT FL220 AND A B737A FROM PIT TO MDW CLBING TO FL260. CTLR IN THE PREVIOUS SECTOR POINTED B737 OUT TO ME. I SAID NO; KEEP HIM CLBING; I'LL TALK TO HIM HERE. MY D-SIDE GOT THE DA10 CTL TO DSND FROM THE PREVIOUS SECTOR. I DSNDED DA10 TO FL180 (I HAD TFC LOWER). I TOLD THE B737 TO KEEP CLBING. I WAS VERY BUSY AT THE TIME WITH CLE ARRS OVER MFD AND APE; ENRTE TFC; CLE ARRS HERE AND COMING. WHEN I LOOKED BACK I REALIZED THAT THE CLB-DSCNT RATIO WASN'T GOING TO WORK. I ASKED FOR RPTS AND TURNED THE DA10 L; SEPARATION WAS LOST AT 700 FT AND 4.7 MI. WHAT I PROBABLY SHOULD HAVE DONE WAS STOP THE B737 AT FL210 AND WAITED UNTIL THEY CLRED AND THEN DSNDED DA10. I DECIDED TO DSND DA10 BECAUSE HE WAS ON ARR AND I HAD TO GET HIM BELOW OTHER ARRS INBOUND TO CLE. THE CORRECT APCH WOULD HAVE BEEN; DA10 AT FL220; B737 AT FL210 AND IF I HAD TO SPIN DA10 TO GET HIM DOWN; THAT WOULD HAVE BEEN BEST.