ZAU CTLR DESCRIBES HOW OPERROR WAS CAUSED BY ZAU 'JOINT USE AIRSPACE.'

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MY FIRST 14 YRS AS A CTLR WERE AT ZOB. THE LAST 2 YRS HAVE BEEN AT ZAU. THE PAST 7 MONTHS HAVE BEEN IN MY CURRENT AREA (NE). ZAU HAS JOINT OR SHARED USE AIRSPACE. TO MY KNOWLEDGE THIS IS IN DIRECT CONFLICT WITH THE 7110.65; AIR TFC PROCS. I'M TOLD EVALUATION TEAMS FROM OUTSIDE THE FACILITY REPRIMAND THEIR USE IN RPTS. THE MGMNT CHOOSES TO IGNORE THEM. THE CPR FALCON WAS ON MY FREQ AT FL190. THE FALCON WAS INSIDE MY SECTOR LATERAL LIMITS IN EXCESS OF 3 MI. HOWEVER; IT TRAVERSED THE 'SHARED' AIRSPACE. THE SECTOR I WAS WORKING HAS THE RESPONSIBILITY TO 'POINT OUT' SUCH ACFT. SINCE THE ADJACENT SECTOR CAN DSND THEIR ACFT IN THIS 'SHARED' AIRSPACE WITHOUT ADVISING ME; THE ADJACENT SECTOR WORKING THE AIRBUS DSNDED IT FROM FL200 TO FL180. BOTH SECTORS WERE UNAWARE OF THE OTHER SECTOR'S TFC. THE AIRBUS BEGINS DSCNT THEN ADVISES OF A TCASII ALERT AND CLBS BACK TO FL200. AS THE AIRBUS LEAVES 19800 FT THE CONFLICT ALERT; SEEING THE DSCNT; ACTIVATES. DUE TO THE LAG IN MODE C RPTING; SEPARATION WAS INCREASING (THANKS TO TCASII) BY THE TIME THE CONFLICT ALERT ACTIVATED. CLOSEST PROX ABOUT 700 FT AND 3.5 MI.