B727 FLC HAS NMAC WITH C172 ON TKOF. ATC CLRED BOTH ACFT AT SAME TIME. NMAC.

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WHILE TAXIING OUT TO THE RWY; WE WERE CLRED FOR TKOF ON RWY 5 WITH THE ADVISORY THERE WAS AN ACFT ON 3 MI FINAL FOR THE SAME RWY. I PARTIALLY ADVANCED THE THROTTLES (APPROX 1.3 EPR) TO MAKE A ROLLING TKOF. AS I WAS LINING UP ON THE RWY AND ADVANCING PWR TO ALTERNATE TKOF EPR; ALL 4 OF US HEARD TWR CLR ANOTHER ACFT FOR TKOF ON RWY 36. OUR TKOF ROLL PROCEEDED WITH NO ACFT SIGHTED; AND THE FO CALLED OUT V1/VR. WE ALL SAW THE CESSNA 172 CLBING OUT ON A 360 DEG HDG OFF RWY 36 AT THIS TIME. WHILE THE FO KEPT THE CESSNA IN SIGHT; I CALLED V2 AND OUR ACFT WAS AIRBORNE. I IMMEDIATELY SHALLOWED OUT THE CLB AND PASSED UNDERNEATH THE CESSNA. THE FO SAID; 'LEVEL OFF' TWICE; AND THE CESSNA APPEARED TO BE DIRECTLY OVERHEAD. I DID NOT RAISE THE LNDG GEAR UNTIL WE WERE CLR OF THE CESSNA; THEN I BEGAN A NORMAL CLBOUT. TWR ASKED IF WE THOUGHT THAT WAS CLOSE; AND THE FO REPLIED; 'YES;' AND ASKED THE TWR TO MARK THE TAPE. THE FLT ATTENDANTS LATER SAID THEY FELT A SHALLOWING OUT OF THE CLB; BUT DID NOT SENSE ANYTHING ABNORMAL. NO PA WAS MADE; AND NO COMMENTS WERE HEARD FROM DEPLANING PAX. ON ARR IN ATL; I CALLED CHIEF PLT; AND INFORMED HIM OF WHAT HAPPENED. HE ASKED ME TO FILE A NMAC RPT WITH BHM TWR WHEN WE RETURNED TO BHM (OUR NEXT LEG). BACK IN BHM; I TALKED WITH FACILITY MGR AND THE ASSISTANT FACILITY MGR. THEY INFORMED ME THAT THE PAPERWORK HAD BEEN STARTED TO FILE AN OPERROR ON THE TWR CTLR; AND THAT THE TWR CTLR HAD BEEN DECERTIFIED. THEY BOTH COMMENDED MY FO FOR HIS PROFESSIONALISM ON THE RADIO AND APOLOGIZED FOR THE INCIDENT. THEY ESTIMATED THE VERT SEPARATION WAS 500 FT. I THEN TALKED WITH WATCH SUPVR; WITH WHOM I FILED THE NMAC RPT. SUPPLEMENTAL INFO FROM ACN 340945: I WAS AN EXTRA CREW MEMBER RIDING ON THE JUMP SEAT OF FLT B727 FROM BHM-ATL. IT WENT THROUGH MY MIND THAT THE TWR MUST BE PLANNING TO TURN THE CESSNA OFF RWY HDG TO AVOID A POSSIBLE COLLISION. NEVER ASSUME.