A LNDG ACR MLG KEEPS A WARY EYE ON LTT IN THE PROCESS OF ABORTING TKOF ON XING RWY.

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WE WERE MAKING A VISUAL APCH TO RWY 36L AT CVG ARPT AND HAD BEEN CLRED TO LAND ON RWY 36L. ANOTHER ACFT HAD BEEN CLRED FOR TKOF ON RWY 27 (AN LTT). WHEN WE WERE ON SHORT FINAL APCH; THE TWR INSTRUCTED THE LTT TO CANCEL TKOF CLRNC. THE LTT CREW RESPONDED 'ROGER; WE ARE ABORTING.' THIS CAUGHT OUR ATTN; BUT IT WAS JUST PRIOR TO OUR LNDG ON RWY 36L. AFTER LNDG ON RWY 36L WE SAW THE ACR LTT BRAKING TO A STOP ON RWY 27 (WHICH INTERSECTS RWY 36L). WE SAW THAT THE OTHER ACFT WAS COMING TO A STOP SAFELY BEFORE THE INTXN SO WE CONTINUED THE LNDG ROLL THROUGH THE INTXN AND CLRED THE RWY AS INSTRUCTED. AFTER CLRING THE RWY; WE ASKED THE TWR CTLR IF THERE WAS ANY PROBLEM; TO WHICH HE RESPONDED; 'NO -- IT WAS MY FAULT.' THIS SITUATION DID NOT CAUSE A SERIOUS CONFLICT; HOWEVER; HAD THE OTHER ACFT BEEN FARTHER ALONG IN THE TKOF ROLL AND NOT BEEN ABLE TO ABORT THE TKOF OR NOT STOP BEFORE THE INTXN OF RWY 36L; IT COULD HAVE CAUSED A VERY SERIOUS CONFLICT. I THINK THE TWR CTLR THOUGHT HE HAD A LITTLE MORE SPACING IN THE TFC SO HE CLRED THE ACFT FOR TKOF AFTER WE HAD BEEN CLRED FOR LNDG; THEN REALIZED IT WAS CLOSER THAN THOUGHT AND HAD THE OTHER ACFT CANCEL THE TKOF CLRNC. WE CONTACTED THE CTLRS AFTER ARR AND DISCUSSED THE SITUATION JUST TO VERIFY THAT EVERYTHING WAS OK AND THAT WE WERE NOT AT FAULT. THEY VERIFIED THAT WE HAD NO FAULT AND THEY WERE GOING TO LISTEN TO THE TAPES JUST TO REVIEW IT TO PREVENT THIS TYPE OF SITUATION FROM OCCURRING AGAIN. I BELIEVE TO PREVENT THIS OCCURRENCE THE TWR CTLR COULD HAVE WAITED TO GIVE THE OTHER ACFT TKOF CLRNC UNTIL WE HAD LANDED. THE OTHER ACFT MAY HAVE TAKEN TOO MUCH TIME INITIATING THE TKOF ROLL -- WHICH WE DO NOT KNOW -- IN WHICH CASE THE TWR COULD HAVE CANCELLED THE TKOF CLRNC SOONER. AT ANY RATE -- WE ARE VERY THANKFUL THAT THERE WAS NOT A CLOSER CONFLICT BTWN US AND THE OTHER ACFT.