FLC OF A B737-300 USED INTO THEIR MINIMUM FUEL DURING DELAYED APCH AT DEST.

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PHX WX 38 BROKEN; 60 OVCT; 10 MI VISIBILITY. WE HAD PROGRESSED THROUGH A SERIES OF HOLDS AND VECTORS WITH A REROUTE FROM THE KARLO ARR TO THE FOSSEL ARR. WITH THIS FINAL EFC FROM ABQ I ADVISED THEM THAT IN 28 MINS (OUR EFC) THAT I WOULD DECLARE 'MINIMUM FUEL' AND EITHER NEED NO DELAYS TO PHX OR I WOULD DIVERT TO OUR LISTED ALTERNATE OF TUS. ABQ THANKED ME FOR MY HEADS-UP. APPROX 5 MINS PRIOR TO OUR EFC WE WERE CLRED INBOUND AND HANDED OFF TO PHX TRACON. UPON INITIAL CONTACT I ADVISED THEM THAT WE WERE VERY CLOSE TO 'MINIMUM FUEL.' PHX ADVISED ME THAT ONE TURN IN HOLDING AT TONTO WOULD BE NEEDED. I RESPONDED THAT WE COULD DO ONE TURN; BUT ANY FURTHER DELAY WOULD PROBABLY CAUSE US TO DIVERT TO TUS. AFTER ONE TURN WE WERE CLRED INBOUND. AT APPROX 8000 FT MSL NEAR THE PHX VOR; WE COULD SEE THE ARPT. AT 6000 FT MSL I COULD CLRLY SEE THE CITY AND SKY HARBOR (PHX) AS WE WERE BELOW THE CLOUD DECK. APCH THEN SENT US OUT W QUITE A WAYS AND HAD US SLOW WHICH WITH GEAR AND FLAPS RESULTED HIGHER FUEL FLOWAS. WE BURNED INTO OUR MINIMUM FUEL (TUS AND 4.0); DURING THIS EXTENSIVE PATTERN; HOWEVER; WE WERE VFR THROUGHOUT.