MD11 CREW RPTS FUEL QUANTITY INDICATION ERROR THAT SHOWS FUEL RAPIDLY DECREASING; CAUSING AN EMER DIVERSION TO NEAREST ARPT.

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NUMEROUS ALERTS OCCURRED DURING CLBOUT; TWO OF WHICH WERE RELATED TO THE FUEL SYSTEM (LEVEL 2 BALLAST FUEL DISAGREE). AFTER LEVEL OFF AT FL260 WE WERE MONITORING THE FUEL SYSTEM SYNOPTIC PAGE ON THE EAD WHEN THE FO COMMENTED ON THE FUEL STATUS; I RECALL SEEING ALL THREE FUEL QUANTITIES RAPIDLY DECREASING PAST 1800 LBS PER TANK. THE FO IMMEDIATELY COMMENTED THAT ZZZ WAS CLOSE AND THAT HE WAS FAMILIAR WITH THE AIRFIELD. AFTER LOOKING AT THE OVERHEAD FUEL PANEL AND CROSS CHKING THE DISPLAYS WITH THE EAD QUANTITIES; I SELECTED NEAREST ARPTS ON THE FMC AND CONFIRMED THAT ZZZ WAS THE NEAREST ARPT; WE STARTED HEADING DIRECTLY FOR ZZZ. I DECLARED AN EMER AND REMEMBERED SEEING 700 LBS REMAINING IN EACH TANK (TANKS 1; 2; 3 WITH THE SAME DISPLAY ON THE OVERHEAD). I RECALL USING THE SATCOM TO NOTIFY DISPATCH OF OUR SITUATION AND INTENTIONS. ATC HANDLING THROUGHOUT WAS OUTSTANDING (CALMING AND PROFESSIONAL). AS WE CROSSED THE THRESHOLD AT ZZZ; I RECALL SEEING 400 LBS PER TANK ON THE EAD. AS WE ROLLED THROUGH 60 KTS THE FUEL QUANTITIES STARTED RAPIDLY INCREASING. WE CLRED THE RWY AND AS REQUESTED CRASH FIRE RESCUE AT ZZZ INSPECTED OUR ACFT FOR EXTERNAL ISSUES SUCH AS FUEL LEAKS. NO VISUAL PROBS WERE REPORTED AND WE TAXIED UNEVENTFULLY TO ZZZ RAMP. OUR BLOCK IN FUEL WAS APPROX 62200 LBS TOTAL (24.2 BALLAST IN UPPER AUX AND 38.0 USEABLE BETWEEN TANKS 1; 2; 3). I AM PERSONALLY AWARE OF ONE OTHER MD11 THAT HAD A SIMILAR PROB AND HAVE HEARD THAT THERE HAS BEEN ANOTHER. A TREND? WHAT STARTED OUT AS RATHER BENIGN FERRY FLT RAPIDLY TURNED INTO A TEST OF OUR CRM AND TRAINING.CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR HAD NO INFO AS TO WHAT EXACTLY CAUSED THE MALFUNCTION BUT HAS SECOND HAND INFO THAT IT HAS OCCURRED ON TWO PREVIOUS OCCASIONS TO OTHER CREWS.