MD80 ON BYP STAR INTO DFW EXPERIENCED TCASII RA BELIEVED TO BE INITIATED BY ACFT CONDUCTING PARACHUTE ACTIVITY NEAR STAR RTE.

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SOMETIME AFTER STARTING A ROUTINE BYP 5 ARR; WE BECAME AWARE THAT ATC EITHER HAD A PEAK IN TFC OR WAS HAVING A LITTLE TROUBLE IN MAINTAINING SPACING. WHILE SOME ADJUSTMENTS USUALLY OCCUR TO FINE TUNE SPACING; WE CHANGED OUR SPD SOME 7 TO 8 TIMES. OTHER ACFT ON THE ARR SEEMED TO BE RECEIVING SIMILAR; SOMEWHAT MORE THAN USUAL ADJUSTMENTS. I WAS ABLE TO DEDUCE WHAT FLT WAS JUST AHEAD SINCE WE GOT THE SAME ADJUSTMENTS RIGHT AFTERWARDS. ONE OF THE LAST ZFW CTLRS ADDED A MODIFIED XING INSTRUCTION TO THE STANDARD ARR. CROSS KARLA INTXN AT 15000 FT; AND LEMYN AT 11000 FT. WE ENTERED THIS INTO THE GPS SYS AND THEN MONITORED THE DSCNT. THE ACFT WAS SET UP BASED ON THOSE XINGS AND WAS RIGHT ON TARGET. THE PRECEDING FLT ADVISES CTR THAT HE IS RESPONDING TO AN RA AND IS CLBING. IN THE CTLR'S EXCHANGE WITH THEM; HE SEEMED SOMEWHAT SURPRISED; BUT WE MISSED THE REST OF THE EXCHANGE. THE FOLLOWING EVENTS ALL OCCURRED AT THE VERY SAME INSTANT: 1) THE CTLR CALLS US AND INSTRUCTS US TO 'STOP' AT 15000 FT. 2) THE ACFT PASSES BOTH KARLA AND 15000 FT. 3) THE TCASII GOES OFF INDICATING TFC; COMMANDS A CLB. WE RESPONDED THAT WE JUST PASSED 15000 FT AND WERE CLBING AND WERE RESPONDING TO AN RA; ALL IN ONE SENTENCE. THE CTLR THEN CALLED OUT TFC AT OUR 2 O'CLOCK POS AND ASKED; 'YOU'RE CLBING?' SEEMING SORTA SURPRISED/ANXIOUS. WE SAID THAT WE WERE AND HAD ONLY GONE ABOUT 50 BELOW; THINKING HE NEEDED ALT VERIFICATION/INFO TO LOOK AT THE SEPARATION FOR THE TFC THAT CAUSED THE RA. HE THEN ASKED IF WE HAD GOTTEN THE 15000 FT XING. AFTER WE SAID WE HAD; WE BOTH LOOKED AT EACH OTHER WONDERING WHY; SINCE WE HAD IN FACT CROSSED AS INSTRUCTED; BUT THEN WERE ASKED TO STOP AT 15000 FT RIGHT AFTER THE XING. JUST AFTER WE VISUALLY SAW TFC THAT WAS AT OUR 2 O'CLOCK POS; BUT HAD PLENTY OF SPACING AND DIVERGENT FLT PATHS. I THINK THE TFC THAT CAUSED ALL OF THIS WAS A CESSNA CARAVAN DOING PARACHUTE WORK. I ALSO THINK HE STRAYED A BIT TOO CLOSE TO THE ARR CORRIDOR ON A BUSY AFTERNOON. I BELIEVE THE CTLR'S PLAN WAS TO USE THE 15000 FT XING TO KEEP SEPARATION; AND ONCE THE FLT AHEAD HAD RESPONDED TO AN RA; HE WANTED TO ENSURE SEPARATION BY STOPPING US AT 15000 FT. OUR COMMENT OF HAVING GONE PASSED 15000 FT (SINCE WE HAD CROSSED THE INTXN) ADDED ONLY CONFUSION. TCASII HAD GONE OFF RIGHT AT 15000 FT; THE ACFT WAS CHANGING FROM ITS DSCNT PROFILE TO A CLB AND TOOK A SMALL AMOUNT OF TIME AND ALT IN DOING SO. TO COMMUNICATE ALL OF THE ABOVE SUCCINCTLY WASN'T OUR HIGHEST CONCERN; SINCE WE WERE BOTH ENSURING RA COMPLIANCE; ATTEMPTING TO GAIN VISUAL CONTACT; AND SITUATIONAL AWARENESS. PERHAPS A MOMENT OR TWO AFTER ALL OF THIS WE WERE TOLD TO CONTACT APCH. I THINK BECAUSE ALL OF THIS OCCURRED VERY CLOSE TO THE CTR/APCH BOUNDARY; THE COORD BTWN CTLRS WOULD HAVE BEEN VERY DIFFICULT. AND AGAIN; WE REALLY DON'T THINK ATC HAD CLRED THAT CARAVAN TO BE WHERE IT ENDED UP. THE TCASII SYS DID A REALLY NICE JOB IN THIS CASE.