B737 CREW HAD A TFC CONFLICT WITH A BEECH BARON DEPING ANC.

Narrative

ON DEP FROM TED STEVENS INTERNATIONAL ARPT; A BEECH BARON WAS CLRED FOR TKOF IN FRONT OF US. THE TWR ASSIGNED HIM A DEPARTURE HDG OF 160 DEG. WE WERE THEN TOLD TO TAXI INTO POS AND HOLD. THE TWR THEN ASKED IF WE COULD MAINTAIN VISUAL WITH THE DEP ACFT AND RESPONDED WITH; YES. THE FO WAS FLYING THE AIRPLANE ON DEP AND WAS COMPLYING WITH THE KNIK 6 DEP PROC. UPON CONTACTING DEP I RPTED THAT THE ACFT IN FRONT OF US WAS IN SIGHT. AFTER ROLLING OUT ON OUR SID HDG OF 190 DEG; IT BECAME EVIDENT THAT WE WERE HDG FOR THE ACFT IN FRONT OF US. DEP WAS TALKING TO ANOTHER ACFT AT THIS TIME AND I WAS GOING TO REQUEST A TURN FURTHER TO OUR RIGHT IN ORDER TO AVOID THE PRECEDING ACFT. DEP CAME ON ABOUT THIS TIME AND TOLD US TO TURN RIGHT IMMEDIATELY TO A HDG OF 270 DEG. THIS WAS GOING TO ALLOW US CLOSE TO THE OTHER ACFT; BUT NOT PUTTING EITHER ACFT IN DANGER. DEP THEN TALKED TO THE BARON; AND ABOUT THIS TIME OUR TCAS WENT OFF; AND I RPTED TO DEP AND WE ENDED UP CLBING THROUGH OUR ASSIGNED ALT. DEP THEN CAME BACK ON TELLING US THAT THEY NEEDED US BACK AT 4000 FT IMMEDIATELY OF WHICH WE COMPLIED. THE FLT THEN CONTINUED ON NORMALLY.