FLC EXPERIENCED DIFFICULTY MAINTAINING RWY HDG DURING TKOF ROLL AND DISCONTINUED THE TKOF.

Narrative

THE MAIN TIRES STRADDLED THE CTRLINE AND THE NOSE WAS WITHIN 20 DEGS OF THE RWY HDG AS I BROUGHT THE ENGS UP TO FLEX TKOF PWR. PLANE AXIS NOW PARALLELED THE CTRLINE. JUST AS WE BEGAN TO ROLL; I TRIED TO STEER THE NOSEWHEEL SO IT WOULD BE EXACTLY OVER THE CTRLINE. THE NOSEWHEEL STEERING TILLER AND PEDAL RESPONSIVENESS THEN BECAME EXAGGERATED. INITIALLY THE STEERING WAS HYPERSENSITIVE AND MOVED THE NOSE TOO QUICKLY. THEN IT SEEMED SLUGGISH AND LACKING IN FINESSE AS I APPLIED CORRECTIVE ACTION. THE ACFT NOSE THEN PERFORMED A DISCONCERTING R/L/R MOTION. ALL THE WHILE IT SEEMED THAT MY COUNTERING HAND/FOOT INPUTS WERE DELAYED IN BEING XFERRED TO THE NOSEWHEEL. IN THE MIDST OF THIS; I CUT THE ENGS BACK TO IDLE; BUT THE SPOOL-DOWN DOES TAKE A FEW SECONDS. BTWN THE RESIDUAL PWR AND MY ASSERTIVE BRAKING THE BIT OF LURCHING WAS OBVIOUSLY NOTICED BY THE PAX. OUR SPD NEVER REALLY EXCEEDED 15-20 MPH. DISCONTINUING THE TKOF; WE INFORMED THE TWR AND TAXIED BACK TO THE GATE WITHOUT ANY MORE STEERING ANTICS. IT'S POSSIBLE THAT THE ENGS SPOOLED UP UNEVENLY; THOUGH I THOUGHT I ADVANCED THEM TOGETHER. AT THE GATE I ASKED THE FO FOR HIS IDEAS AND THEN HAD ALL THE WHEELS; STRUTS; AND HYD FLUIDS CHKED OVER. THERE WEREN'T ANY INJURIES; BUT 2 PAX DECIDED TO DISEMBARK. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THAT THE TKOF ROLL BECAME VERY DIFFICULT TO CTL AND HE REJECTED THE TKOF. AFTER RETURNING TO THE GATE; MAINT INSPECTED THE ACFT AND COULD FIND NO INDICATION OF A CTL PROB. THE RPTR ELECTED TO TAKE THE ACFT TO DEST AND EXPERIENCED NO CTL DIFFICULTIES.