Narrative:

Late night departure from dfw. The tower was conducting parallel and simultaneous departures from 35L and right. We were cleared into position on 35R and holding for wake turbulence sep from a heavy transport that had just departed from 35L. Also an medium large transport was holding in position for 35L. Tower cleared us to takeoff on 35R and turn to 345 degrees. After lift-off passing 300', we turned to 345 degrees and the tower called and said to turn right to 360 degrees. I looked out my left window and just below and off to the left was our company medium large transport climbing out from 35L. We turned to 360 degrees and were advised to contact departure. Prior to switching, I asked the tower to confirm that our initial heading was 345 degrees. He replied that it was and he made a mistake in assigning a heading that would drift us into another runway and aircraft. 1) we should have questioned the heading initially, but we were unaware that a simultaneous departure would take place and it was the first time in 11 yrs I had seen that type of operation at dfw. 2) since the other airplane was beyond my peripheral vision and we were busy with cockpit duties during the initial climb, the incident could have been much more serious. 3) in the future, I will question any heading that will cause me to drift into other runway's operations.

Related reports:

Google
 

Original NASA ASRS Text

Title: DEP HEADING ASSIGNED BY ATC LCL CTLR RESULTS IN CONFLICT BETWEEN 2 ACR MLG DEPARTING PARALLEL RWYS.

Narrative: LATE NIGHT DEP FROM DFW. THE TWR WAS CONDUCTING PARALLEL AND SIMULTANEOUS DEPS FROM 35L AND R. WE WERE CLRED INTO POS ON 35R AND HOLDING FOR WAKE TURB SEP FROM A HVT THAT HAD JUST DEPARTED FROM 35L. ALSO AN MLG WAS HOLDING IN POS FOR 35L. TWR CLRED US TO TKOF ON 35R AND TURN TO 345 DEGS. AFTER LIFT-OFF PASSING 300', WE TURNED TO 345 DEGS AND THE TWR CALLED AND SAID TO TURN RIGHT TO 360 DEGS. I LOOKED OUT MY LEFT WINDOW AND JUST BELOW AND OFF TO THE LEFT WAS OUR COMPANY MLG CLBING OUT FROM 35L. WE TURNED TO 360 DEGS AND WERE ADVISED TO CONTACT DEP. PRIOR TO SWITCHING, I ASKED THE TWR TO CONFIRM THAT OUR INITIAL HDG WAS 345 DEGS. HE REPLIED THAT IT WAS AND HE MADE A MISTAKE IN ASSIGNING A HDG THAT WOULD DRIFT US INTO ANOTHER RWY AND ACFT. 1) WE SHOULD HAVE QUESTIONED THE HDG INITIALLY, BUT WE WERE UNAWARE THAT A SIMULTANEOUS DEP WOULD TAKE PLACE AND IT WAS THE FIRST TIME IN 11 YRS I HAD SEEN THAT TYPE OF OPERATION AT DFW. 2) SINCE THE OTHER AIRPLANE WAS BEYOND MY PERIPHERAL VISION AND WE WERE BUSY WITH COCKPIT DUTIES DURING THE INITIAL CLB, THE INCIDENT COULD HAVE BEEN MUCH MORE SERIOUS. 3) IN THE FUTURE, I WILL QUESTION ANY HDG THAT WILL CAUSE ME TO DRIFT INTO OTHER RWY'S OPS.

Data retrieved from NASA's ASRS site as of July 2007 and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.