ACR CV60 DEPARTING CVG; AT ROTATION; SPOTS A C310 IN POS MIDFIELD. PLT PULLED UP QUICKLY AND MADE A SLIGHT TURN TO MISS THE CESSNA.

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THE FO CALLED CVG TWR ON 118.3 THAT WE WERE READY FOR TKOF RWY 18L. THE TWR CLRED US FOR TKOF AND THE FO READ BACK THE CLRNC. THE FO WAS FLYING AND I WAS WATCHING THE ENG GAUGES AND MAKING AIRSPD CALLS. I LOOKED UP JUST AS I HAD CALLED ROTATE AND THE FO WAS STARTING TO ROTATE. I SAW A TWIN CESSNA SITTING ON THE RWY IN FRONT OF US. I TOOK THE CTLS AND PULLED THE PLANE OFF AND MADE A SLIGHT R TURN CLRING THE CESSNA. ONCE AIRBORNE; I CALLED THE TWR TO VERIFY WE WERE CLRED FOR TKOF. HIS RESPONSE WAS; YOU'RE AIRBORNE AREN'T YOU? I REPLIED YES AND TOLD HIM THERE WAS A PLANE SITTING ON THE RWY ABOUT MIDFIELD. HE ASKED IF WE WERE ALL RIGHT; I SAID YES; AND WE WERE. HE SAID; SORRY ABOUT THAT; THEN ANOTHER CTLR CAME ON AND CLRED US TO DEP. NEITHER THE FO NOR MYSELF HEARD ANY XMISSION BTWN THE TWR AND THE CESSNA. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED HE HAD NO FURTHER CONTACT WITH CVG TWR PERSONNEL. A COMPANY RPT WAS FILED. THE CHIEF PLT CALLED THE AIR TFC MGR ABOUT THE INCIDENT. THE TWR REPRESENTATIVE ACKNOWLEDGED RESPONSIBILITY AS CTLR ERROR. THE RPTR IS NOT AWARE OF ANY FURTHER FOLLOW-UP ACTION.