A ZLC ARTCC RADAR CTLR LOST SEPARATION BTWN AN LJ40 AND AN A300 IN HIS SECTOR AT FL360.

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ACFT #1 WAS BEING VECTORED AND DSNDED TO HIS DEST; 36U. 2 OTHER ACFT WERE IN HIS WAY. AS I GAVE ACFT #1 HIS LAST DSCNT CLRNC; I RECEIVED A CONFLICT ALERT ON OTHER TFC IN MY SECTOR. THE ALERT WAS FOR ACFT #1 AND ACFT #2 HAVING LOST SEPARATION. THIS WAS THE FIRST TIME I HAD SEEN ACFT #2. SIMULTANEOUSLY ACFT #2 CALLED TO SAY HE WAS RESPONDING TO AN RA AND ASKED ABOUT THE TFC. THAT WAS WHEN I NOTICED THAT ACFT #2 WAS IN THE HDOF MODE TO ANOTHER SECTOR. WE HAD RECENTLY COMBINED ANOTHER SECTOR WITH MINE. THE PERSON CLOSING THE OTHER SECTOR HAD HANDED OFF ACFT #2 TO THE WRONG SECTOR AND SO IT DID NOT DISPLAY ON MY SCOPE UNTIL THE CONFLICT ALERT FORCED IT TO MINE. I HAD NO KNOWLEDGE OF ACFT #2 UNTIL THE CONFLICT ALERT. THIS EVENT HAPPENED VERY NEAR THE CONVERGENCE OF 8 DIFFERENT SECTORS BTWN 2 CTRS. IT WAS MY FIRST DAY BACK AFTER 3 WKS OFF. I WAS BEING ESPECIALLY CAREFUL; BUT DID NOT SEE THE LIMITED DATA BLOCK THROUGH A LOT OF OTHER DATA BLOCK CONGESTION. ONE PRACTICE I USE IS WHEN I CLOSE A SECTOR (COMBINING MY AIRSPACE WITH ANOTHER SECTOR; GIVING MY TFC TO THEM); I ALWAYS MAKE SURE I CAN DROP ALL OF MY DATA BLOCKS. IF I CAN DROP THEM THEN SOMEONE ELSE HAS TAKEN CTL OF THEM AND THEY HAVE ALL BEEN ACCOUNTED FOR. AFTER REVIEWING THE TAPES IT WAS DISCOVERED THAT ACFT #2 NEVER CHKED IN WITH US. HIS FIRST CALL TO THE CTR WAS TO ASK ABOUT THE RA. MY ASSUMPTION IS THAT HE DIALED IN OUR FREQ; HEARD THAT WE WERE BUSY; WAITED FOR AN OPPORTUNITY TO JUMP IN AND THEN FORGOT. DON'T KNOW IF THAT MADE A DIFFERENCE OR NOT. MY SECTOR WAS GOING RED AS THE DECISION WAS MADE TO COMBINE THE OTHER WITH MINE. OUR TMU MONITORS THE SECTORS TO TRY AND PREDICT (AND HOPEFULLY PRECLUDE) OVERLOADING. THAT PROCESS DIDN'T WORK. IT SHOULDN'T HAVE BEEN COMBINED; BUT WE WERE RUNNING SHORT OF CTLRS ON THIS SHIFT SO CORNERS MAY HAVE BEEN CUT.