MLG ON CLBOUT HAS TCASII RA DUE REROUTE DEPS.

Narrative

WHILE CLBING TO 10000 FT ON DEP FROM DFW AN RA ON TCASII WAS RECEIVED WHICH HELPED PREVENT A POTENTIAL NEAR MISS SIT. THE WX CONDITIONS IN THE LCL AREA REQUIRED ATC TO RERTE ACFT TO BASICALLY 1 DEP RTE. WE DEPARTED DFW BEHIND AN ACR A 757 ACFT WHICH HAD DEPARTED AFTER AN ACR B 737. WE WERE CLRED TO CLB TO 10000 FT; HDG 050 DEGS TO INTERCEPT THE DFW 067 DEG RADIAL. PASSING 9100 FT A TA WAS RECEIVED SHOWING TFC AT 2 O'CLOCK AND 5 MI; AND 900 FT ABOVE. AT 9400 FT A RA WAS RECEIVED WITH A COMMAND TO DSND. WHEN INITIATING THE DSCNT; THE 757 WAS ACQUIRED VISUALLY AT 10000 FT AND LESS THAN 2 MI. A CLR OF CONFLICT ADVISORY WAS THEN GIVEN AND THE CLB TO 10000 FT WAS CONTINUED. ATC WAS NOTIFIED OF OUR RA ACTIONS. AT NO TIME DID ATC ISSUE TA'S OR INQUIRE AS TO OUR ALT. EARLIER DURING THE CLB; ATC HAD AMENDED ACR B'S CLB INSTRUCTIONS FROM 10000 FT TO 9000 FT. MOMENTS LATER; ACR B WAS THEN INSTRUCTED TO ACCELERATE TO 300 KTS DEPARTING 10000 FT. THEY RESPONDED WITH 'ROGER; BUT WE ARE ONLY CLRED TO 9000 FT.' THEY WERE THEN CLRED TO 17000 FT. ALL 3 ACFT WERE FLYING BASICALLY THE SAME ROUTING. I BELIEVE THAT OUR TURN AFTER TKOF FROM A HDG OF 170 TO 080 TO 050 DEGS PUT US INSIDE THE TURN OF THE 757. THE 757 WAS HDG APPROX 360 DEGS WHEN VISUAL CONTACT WAS MADE. I ALSO BELIEVE THAT ATC HAD INTENDED TO ISSUE US AN AMENDED CLRNC TO 9000 FT BUT GAVE THAT CLRNC TO ACR B. IT APPEARED THAT DEP CTL WAS TRYING TO EXPEDITE THE DEPS FROM DFW WHAT WITH THE POSSIBILITY OF TSTMS APCHING THE AREA. ALSO; 1 DEP RTE WAS CLOSED DUE TO WX ALONG THAT RTE. AS A CONSEQUENCE; ATC WAS REROUTING WHICH PUT MORE ACFT THAN NORMAL ON 1 RTE. IT IS POSSIBLE THAT THE CTLR'S WORKLOAD INCREASED TO A POINT WHERE HE ISSUED AN AMENDED CLRNC TO THE WRONG ACFT.