ACR FLC ON TKOF FROM PHX ARE AGAIN CLRED FOR TKOF AFTER AIRBORNE. PIC BELIEVES LCL CTLR CONFUSION DUE TO TFC VOLUME.

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I WAS THE CAPT OF ACR X FROM PHX TO CMH. THE PUSHBACK AND TAXI OUT WERE NORMAL. WE TAXIED TO RWY 25R; WHERE THE DIFFERENT TXWYS FEED THE DEP END OF RWY 25R. IT WAS THE AFTERNOON RUSH AND THE LCL CTLR WAS VERY; VERY BUSY. THE NORMAL PROCS WHEN THE ARPT IS IN THIS CONFIGN IS FOR ACFT TO RPT ONE AFTER ANOTHER ON RWY 25R; WITH TKOF CLRNCS COMING JUST AFTER THE PRECEDING ACFT WAS ROTATED. WHILE THIS IS HAPPENING; ARRIVING ACFT ARE DOING VISUAL APCHS TO RWY 25R BUT AT ABOUT 3 MI THE LCL CTLR SIDE-STEPS THE ARRIVING ACFT TO RWY 25L. WHEN MY FLT WAS #1 AT THE END OF THE RWY; THE CTLR CLRED US 'INTO POS AND HOLD RWY 25R.' I TAXIED THE ACFT ONTO THE RWY AND WAS JUST ABOUT TO MAKE THE 90 DEG TURN ON THE RWY FOR THE 'HOLD POS' WHEN THE CTLR CLRED OUR FLT FOR TKOF. I THEN TURNED ON THE LNDG LIGHTS AND THE FO STARTED THE CLOCK; THE PRECEDING ACFT WAS JUST STARTING TO CLB OUT. LIKE I SAID; THE CTLR WAS VERY; VERY BUSY. THE TKOF WAS NORMAL AND I DO NOT FULLY REMEMBER ALL OF THE RADIO CONVERSATIONS DURING THE TKOF ROLL; BUT I DO REMEMBER THE CTLR HAVING A PROB WITH AN ACFT THAT WAS ON AN APCH TO RWY 25R THAT WOULD NOT CHANGE OVER TO RWY 25L. THERE AS WE WERE CLBING OUT OF 500 FT AGL; WITH THE CTLR TALKING NON-STOP; THE FOLLOWING CLRNC WAS ISSUED: 'ACR X CLRED FOR TKOF RWY 25R' FOLLOWED BY THE CTLR RETURNING BACK TO THE ACFT (ACR Z) THAT WOULD NOT SIDE-STEP TO RWY 25L. THE RADIO FREQ WAS SO BUSY WITH THE CTLR AND THAT OTHER ACFT I COULD NOT GET A WORD IN EDGEWISE TO QUERY THAT CLRNC (THE FO WAS FLYING THE PLANE). WE HAD CLBED TO WELL OVER 1000 FT AGL BEFORE THERE WAS A BREAK ON THE RADIO. WHEN THAT BREAK DID HAPPEN; A FOLLOWING COMPANY FLT (ACFT W) ASKED FOR VERIFICATION THAT THEY 'WERE CLRED FOR TKOF.' FOR THE FIRST TIME THE CTLR SOUNDED CONFUSED. SHE THEN CLRED THE FOLLOWING COMPANY FLT FOR TKOF BECAUSE TFC WAS ON A 1 1/2 MI FINAL FOR RWY 25R. THE CTLR THEN CLRED OUR FLT AND THE PRECEDING FLT OVER TO DEP CTL. SEPARATION WAS NEVER A PROB AS ALL 3 ACFT (OUR FLT; THE PRECEDING FLT AND THE FOLLOWING FLT) WERE ALL AT THE NORMAL POS FOR THIS ARPT CONFIGN. AS A MATTER OF FACT; THE FOLLOWING ACFT WAS SEVERAL SECONDS BEHIND WHERE IT NORMALLY WOULD BE. I THINK THE CTLR WAS JUST BEING OVER TAXED AT THAT TIME; WITH ALL OF THE TFC AND THE ARRIVING ACFT THAT WOULD NOT SIDE-STEP TO RWY 25L. THERE WERE ALSO SEVERAL CLOSE SOUNDING FLT NUMBERS THAT DAY TOO.