PLT OF BARON 58 HAS FUEL FLOW PROBS WITH FUEL INDICATOR MALFUNCTION RESULTING IN A ROUGH RUNNING ENG. HE DIVERTS TO NEARBY ARPT.

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RTE FROM NASHVILLE TO KNOXVILLE AT 9000 FT; THE R ENG FUEL FLOW ON A BARON 58 STARTED TO FLUCTUATE FROM 15 GPH TO 5 GPH. THE ENG THEN QUIT. THE FUEL GAUGE SHOWED A LITTLE OVER 1/4 FULL ON R AND ALMOST 1/2 ON THE L SIDE. RESTARTED THE ENG AND IT WAS RUNNING ROUGH AND WOULDN'T MAINTAIN PWR. AT THAT POINT I TOLD ATC THAT I WAS GOING TO LAND AT UPPER CUMBERLAND REGIONAL WHICH WAS ABOUT 5 MI TO THE E. IN THE DSCNT THE ENG STARTED TO SURGE AGAIN AND I SHUT IT DOWN AND SECURED IT FOR LNDG. ON THE GND; HAD FUEL ADDED -- 30 GALLONS A SIDE. THE L SIDE SHOWED AN INCREASE; WITH NO INCREASE ON THE R SIDE. WHEN LEAVING NASHVILLE; BOTH SIDES SHOWED OVER 1/2 FULL -- BTWN 1/2 AND 3/4 FULL. CALLED BACK TO HOME BASE AND THEY SENT ANOTHER ACFT AND A MAINT PERSON TO PICK UP THE PAX AND CHK THE ACFT. THE ENG WAS CHKED OUT AND A RUN-UP WAS COMPLETED. THE RUN-UP CHK WAS NORMAL EXCEPT FOR THE R ENG FUEL FLOW WAS 4-5 GALLONS HIGHER THAN THE L AND IT SEEMED TO BE RUNNING ROUGH. THE ACFT WAS THEN FLOWN BACK TO HOME BASE. NO OTHER PROBS. THE ACFT WAS CHKED BY MAINT AND FOUND SOME PROBS WITH THE FUEL INDICATING SYS. PROBABLE CAUSE WAS FUEL STARVATION DUE TO FAULTY FUEL QUANTITY SYS.