OPERROR. LOSS OF SEPARATION BTWN ACR X AND ACR Y.

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OUR TKOF CLRNC FROM DFW AS 'CLRED FOR TKOF RWY 18L; TURN L HDG 155 DEGS.' FO WAS FLYING. AFTER RETRACTING FLAPS FROM 5 DEGS TO 1 DEG; I (THE CAPT) LOOKED OUT MY L SIDE WINDOW TO LOOK FOR TFC AND NOTICED THAT WE WERE CONVERGING WITH AN MD80 WHO WAS DEPARTING OFF RWY 17R. I ASKED THE DEP CTLR; 'HEY; WHAT IS THAT MD80 DOING? WE'RE HEADING TOWARDS HIM.' AT THIS TIME THE CTLR DID NOT HAVE THAT ACFT ON RADAR AND QUESTIONED MY STATEMENT; FOLLOWED BY HIS STATEMENT OF SOMETHING LIKE; 'WELL; TURN TO AVOID HIM.' (GEE THANKS.) WE TURNED TO 190 DEGS TO INCREASE SPACING. SOON AFTER OUR MAKING THE TURN THE DEP CTLR GOT THE MD80 IN RADAR CONTACT AND PROVIDED SEPARATION. AT NO TIME DID I FEEL THAT OUR ACFT WAS IN DANGER; AND THE 'AVOIDANCE' TURN WAS NOT EXCESSIVE IN BANK RATE OR ANGLE. I DO NOT BELIEVE THAT THE ACFT WOULD HAVE COLLIDED HAD WE NOT MADE THE TURN; BECAUSE THE MD80 WAS ACCELERATING QUICKER THAN WE WERE. I HAVE SUBSEQUENTLY FOLLOWED UP WITH DFW QUALITY ASSURANCE AND WAS TOLD THAT THEIR INVESTIGATION REVEALED THAT THE W LCL CTLR DID; IN FACT; COORDINATE OUR TURN WITH THE E LCL CTLR. HOWEVER; IT APPEARS THAT THE E CTLR 'GOT CONFUSED' AND THOUGHT THAT A PREVIOUS ACFT DEP WAS OURS. THEREFORE; ONCE THAT ACFT DEPARTED HE THOUGHT THAT HE NO LONGER NEEDED THE SLOT SO HE CLRED THE MD80 FOR TKOF. I BELIEVE THAT IT IS NOTEWORTHY THAT TCASII NEVER SOUNDED. AT OUR CLOSEST POINT OF APCH; THE 2 ACFT 100 VERTLY AND 3/4 MI LATERALLY.