A TRACON CTLR WAS INVOLVED IN AN OPERROR WHEN VECTORING A DC10 THROUGH ANOTHER CTLR'S AIRSPACE; DSNDED THE DC10 THROUGH THE ALT OF AN E120; 1000 FT BELOW THE DC10. AT LEAST ONE OTHER CTLR WAS AUTH TO UTILIZE THE SAME PROC. BOTH CTLRS 'QUICK LOOKED' THE ADJOINING AIRSPACE; NOT SEEING EACH OTHER'S TRANSITIONING ACFT.

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ACR X; DC10; 40 MI NW OF ORD; AT 10000 FT INBOUND TO LAND. ACR Y; E120; 4 MI AHEAD OF ACR X; AT 9000 FT ALSO INBOUND TO LAND; BEING WORKED BY A DIFFERENT ARR CTLR; AND ON A DIFFERENT ARTS III DATA BLOCK TAG (F) SYMBOL. ACR X WAS ON A (Z) SYMBOL. I WAS WORKING ACR X AT MY POS AND DSNDED ACR X TO 8000 FT; FAILING TO SEE ACR Y AHEAD AND TO THE L OF ACR X'S POS. I WAS NOT 'QUICK LOOKING' ALL OF THE (F) POS SYMBOLS; AND ACR X AND ACR Y'S TAGS WERE OVERLAPPED AT THE TIME OF DSCNT. ACR X WAS SLOWLY OVERTAKING ACR Y. THE RESULTANT LOSS OF SEPARATION BECAME ACR X 1 NM BEHIND ACR Y AT 9400 FT. ACR Y WAS AT 9000 FT BEFORE ACR X SAW THE TFC AND WAS TOLD TO MAINTAIN VISUAL SEPARATION. I HAD JUST COME IN FOR THE SHIFT AND HAD BEEN WORKING THIS POS FOR ONLY 1 HR AND 10 MINS. MY HDOF CTLR ADVISED ME TO WATCH FOR AND MISS ACFT ON THE 'F' SYMBOL; BEING VECTORED TO ANOTHER RWY. I SIMPLY THOUGHT I HAD SEEN ALL THE APPLICABLE TFC BEFORE DSNDING ACR X; BUT DID NOT SEE ACR Y. I SHOULD HAVE KEPT ACR X AT 10000 FT; AS THERE WAS NO HUGE RUSH TO DSND HIM YET. I WAS DOING THIS AS A REPETITIVE FUNCTION OF CONTINUITY FOR ALL MY ACFT.