A B737 FLAP ASYMMETRY OCCURRED ON FINAL APCH TO A SHORT RWY. CAPT REQUESTED VECTORS TO NEARBY ARPT WITH LONGER RWY. AN EMER WAS DECLARED.

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WE WERE CONFIGURING TO LAND AT ZZZ. WHEN SELECTING FLAPS 5 DEGS; WE NOTICED THE TRAILING EDGE FLAP INDICATOR NEEDLES WERE STUCK BTWN 2 DEGS AND 5 DEGS. WE WERE AROUND 7 MI TO THE FIELD AND THE FLAP LEVER WOULD NOT MOVE THE FLAPS SO WE EXECUTED A GAR AND TOOK A RWY HDG OUTBOUND AND EVENTUAL RADAR VECTORS FOR AN EXTENDED TFC PATTERN TO SET UP FOR ANOTHER APCH TO RWY 2. THE FLAPS WOULD NOT RETRACT ON THE GAR; SO WE WERE LIMITED TO 210 KTS. WHEN EVALUATING THE PROB WE NOTICED THAT THE NEEDLES WERE VERY SLIGHTLY SPLIT AND THERE WAS NO ABNORMAL ROLL. AFTER SOME DISCUSSION ABOUT WHICH FLAP QRH CHKLIST TO USE WE DECIDED ON USING THE 'TRAILING EDGE FLAP DISAGREEMENT' CHKLIST. WE WERE ALSO VERY AWARE OF HOW MUCH FUEL WE HAD ON BOARD. AROUND 7200 LBS BECAUSE WE HAD TANKERED FUEL FOR THE ROUND ROBIN WHICH ORIGINATED IN ZZZ1 THEN PROCEEDED ZZZ-ZZZ2-ZZZ-ZZZ1. WE USED UP 1100 LBS FROM OUR MINIMUM OF 8100 LBS REQUIRED IN ZZZ2 FOR ZZZ. ATC GAVE US VECTORED HOLDING OVER VOR WHILE WE CONTACTED DISPATCH FOR LNDG DISTANCE INFO. THE DISPATCHER DID NOT HAVE A CONCRETE NUMBER AND RECOMMENDED WE GO TO ZZZ2 AND MENTIONED WE WOULD HAVE ENOUGH FUEL TO GET THERE WITH THE FLAPS EXTENDED TO 2 DEGS. WE CONCURRED AND DECIDED TO DIVERT TO ZZZ2 WHERE THE WX WAS VFR AND THERE WAS A LONG RWY. WE HAD REQUESTED AND RECEIVED CLRNC FROM DEP TO ZZZ2. INFLT WE DID HAVE SOME TIME TO CONSIDER A PLAN B IN CASE THE ALTERNATE FLAP DID NOT DO THE JOB FOR US; NO ASYMMETRY PROTECTION; AND DECIDED TO USE THE 'FLAPS BTWN 1-15 DEGS; VREF 40+30' TARGET SPD IF WE NEEDED TO AND WROTE THE NUMBER ON PAPER. WHEN BEGINNING TO EXTEND THE FLAPS ON APCH TO ZZZ2; THE NEEDLES INITIALLY MOVED TOGETHER AND THEN VERY QUICKLY SPLIT. WE ENCOUNTERED NO ABNORMAL ROLL. WE STOPPED USING THE ALTERNATE FLAP SYS AND SET OUR REF 40 + 30 NUMBER IN AND PROCEEDED TO LAND IN ZZZ2 WITHOUT FURTHER INCIDENT. WE DID REQUEST THE EMER EQUIP TO STAND BY AS A PRECAUTION AND THE FLT ATTENDANTS AND PAX WERE BRIEFED THROUGHOUT THE FLT ON OUR SITUATION AS IT UNFOLDED. PLT SCAN OF THE TRAILING EDGE FLAP INDICATOR. WE KNEW THAT WE HAD TO GO AROUND. WE WERE DISTINCTLY AWARE THAT WE HAD A FUEL AND LNDG DISTANCE PROB ON OUR HANDS AND NEEDED ADDITIONAL INFO TO DETERMINE THE BEST ARPT TO LAND. POSSIBLE ASYMMETRY PROTECTION SYS ENGAGED SLIGHTLY PREMATURELY OR OTHER MALFUNCTION OF THE FLAP SYS OR THE TRAILING EDGE FLAP INDICATOR. THE PROB WAS NOT DETERMINED BY THE MECHS IN ZZZ2 WHEN THE CREW LEFT TO DEADHEAD ON A FLT TO ZZZ1.