A DSNDING ACR PASSES ITS HOLDING POINT AT BDF WHILE THE CREW IS ATTEMPTING TO COORDINATE A DIVERSION TO MKE BECAUSE OF TFC DELAYS AND LOW FUEL SIT.

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CLRED BDF.BDF3 TO ORD; HOLD AS PUBLISHED. INFORMED CTR UNABLE TO HOLD DUE TO FUEL STATE. CLRED TO DSND TO FL270. DURING DSCNT; CTR ASKED IF WE COULD GO JVL.JVL4; WE SAID WE COULD BUT QUICKLY CHANGED OUR MINDS TO DIVERT TO MKE AND INFORMED CTR. AS WE PASSED BDF (APPROX 1 MIN E) CTR ASKED IF WE WERE ENTERING THE HOLD AND GAVE US A 180 DEG HDG AND DSCNT TO FL240. WE ARE NOT SURE IF WE WERE CLRED TO JVL; NEGATING THE HOLDING OR NOT. ALL THIS HAPPENED WHILE IMC -- ICING; DEVIATING AROUND TSTMS; CALCULATING FUEL AND COORDINATING A DIVERT. HIGH WORKLOAD IN A 2 MAN COCKPIT. SUPPLEMENTAL INFO FROM ACN 434892: WE WERE GIVEN HOLDING AT BDF. WE INFORMED ZAU THAT WE HAD NO FUEL TO HOLD AND ASKED IF THE EFC WAS FIRM. THEY INFORMED US THAT IT WAS FOR THE BDF ARRS; BUT WE COULD GET RIGHT IN IF WE COULD GO TO JVL AND FLY THE JVL ARR. CTR TOLD US THAT WE COULD NOT GO TO MKE UNTIL WE WERE LOWER AND THEN ASKED IF WE HAD ENTERED HOLDING. CTR GAVE US A TURN TO 180 DEGS THEN LATER BACK TO MKE. THERE WAS MUCH CONFUSION CTRED AROUND THE JVL ARR; BDF ARR; AND MKE DIVERT. THE ERROR WAS MINE IN MISSING BDF HOLD FIX. EXTENUATING CIRCUMSTANCES WERE: WX; DIVERT; ICING; TURB; POSSIBLE CHANGE OF ARR AND FUEL.