FLT CREW OF CE680 TAKE OFF AT NIGHT FROM UNCTLED FIELD AND OBSERVE PREVIOUS LNDG ACFT JUST EXITING THE RWY AFTER THEY BECOME AIRBORNE.

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OUR FLT WAS DEPARTING PWK ARPT FOR CLE ARPT AT XA45. I WAS PERFORMING THE DUTIES OF PF. THE TWR HAD CLOSED 45 MINS EARLIER AND CLRNCS WERE HANDLED BY ORD DEP CTL THROUGH A REMOTE FREQ. WX WAS GOOD AT PWK WITH WINDS ABOUT 10 KTS DIRECTLY ACROSS RWY 16/34. WE HAD RECEIVED OUR IFR CLRNC AND TAXIED TO RWY 34 AS THIS RWY WOULD RESULT IN LESS MANEUVERING FOR AN EBOUND DEP THROUGH CHICAGO AIRSPACE. WE WERE MONITORING CTAF AND A CONQUEST RPTED A L BASE FOR RWY 16. WE OBSERVED THE ACFT ON BASE AND SINCE WE HAD NOT RECEIVED A 'RELEASE' FROM DEP CTL; WE HELD SHORT OF RWY 34. WE WATCHED THE ACFT LAND AND ABOUT THE TIME HE WAS TOUCHING DOWN; DEP CTL NOTIFIED US THAT WHEN HE LANDED WE WOULD BE RELEASED. WE TOLD THE CTLR WE HAD THE ACFT IN SIGHT AND THAT HE WAS LNDG RWY 16 AT THAT MOMENT. FROM OUR POS AT THE HOLD SHORT BARS AT THE OPPOSITE END OF THE RWY; WE CONTINUED TO WATCH THE ACFT'S ROLLOUT AND IT APPEARED THAT HE WAS CLRING THE RWY AS HIS LNDG LIGHTS TURNED TOWARDS US AND WE ASSUMED HE WAS CLRING THE RWY ONTO THE PARALLEL TXWY. BOTH OF US COMMENTED; 'OK; HE'S CLRING THE RWY.' DEP CTL RELEASED US AND WE TAXIED INTO POS. THE PNF SAYS HE ANNOUNCED OUR TKOF ON CTAF ALTHOUGH I CANNOT REMEMBER WHETHER HE DID OR NOT. I LOOKED DOWN THE RWY AND IT APPEARED CLR TO ME. TKOF WAS NORMAL WITH PROPER CALLOUTS. AS I ROTATED THE ACFT; THE PNF SAID; 'IS THAT AN AIRPLANE ON THE RWY?' WE WERE JUST AIRBORNE AT THAT POINT AND JUST AHEAD TO THE LEFT OF OUR ACFT WAS ANOTHER AIRPLANE EXITING THE RWY ONTO A TXWY. AS WE RETRACTED THE GEAR; WE HEARD THE OTHER PLT SAY; 'DIDN'T YOU SEE US?' THE PNF RESPONDED THAT WE HAD NOT SEEN THEM AND THAT THEY SHOULD HAVE BROADCAST THEIR POS ON THE RWY OVER CTAF. THE OTHER PLT RESPONDED; 'WELL ACTUALLY WE DID' WHICH NEITHER OF US REMEMBER HEARING. LOOKING BACK ON THE INCIDENT; IF THE AIRPLANE IN QUESTION WAS INDEED THE CONQUEST THAT HAD JUST LANDED; THEN HE EITHER CLRED THE RWY; TAXIED N ON THE PARALLEL TXWY; AND RE-ENTERED THE RWY TO CROSS TO THE W SIDE OF THE ARPT OR HE MADE A 180 DEG TURN ON THE RWY AND BACK-TAXIED TO THE TXWY TO EXIT THE RWY. EITHER SCENARIO WOULD EXPLAIN WHY OUR OBSERVATION OF HIS LNDG LIGHTS INDICATED HE WAS CLRING THE RWY. BOTH THE PNF AND MYSELF WERE SURE THE RWY WAS CLR WHEN WE STARTED OUR TKOF ROLL. WE BOTH LOOKED DOWN THE RWY AND DID NOT OBSERVE ANYONE ELSE ON OR APCHING THE RWY. WE WERE POSITIVE THE RWY WAS CLR. IT IS POSSIBLE THE OTHER ACFT IN QUESTION HAD TURNED OFF HIS LNDG LIGHTS; WHICH MADE HIM LESS VISIBLE. IF THIS WAS THE CASE AND HE HAD MADE THE 180 DEG TURN; THEN ONLY HIS TAIL NAV LIGHT AND BEACON WOULD HAVE BEEN VISIBLE. IN ANY EVENT; WE BOTH THOUGHT HE HAD CLRED THE RWY. IN RETROSPECT; IT WOULD HAVE BEEN PRUDENT FOR US TO SPEAK DIRECTLY TO THE OTHER PLT ON CTAF ABOUT HIS POS AND INTENTIONS. IT'S POSSIBLE THAT HE DID NOT EVEN KNOW WE WERE THERE WAITING FOR TKOF AS WE WERE HOLDING ON THE FAR END OF THE RWY WITH ONLY OUR NAV LIGHTS AND ROTATING BEACON. UNCTLED ARPTS LATE AT NIGHT POSE ADDITIONAL RISKS THAT CALL FOR PLTS TO PAY CLOSE ATTN TO TFC AND NOT ASSUME ANYTHING. A LONGER TKOF ROLL OR AN ABORT MIGHT HAVE CHANGED THE OUTCOME OF THIS OP.