ACR FLC ADVISES ZAB CTLR OF MULTIPLE WX DEVS AND CONFLICTS WITH OTHER DEVIATING TFC.

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WE WERE VERY BUSY DEVIATING AROUND NUMEROUS TSTMS WITH LITTLE ROOM TO MANEUVER. AFTER BEING HANDED OFF TO A NEW CTLR; WE INFORMED HIM WE WERE DEVIATING AND RECEIVED HIS PERMISSION. OUR RTE (PLANNED) WAS APPROX 5-10 MI TO OUR R. AS WE BROKE OUT OF SOME CLOUDS; ADDITIONAL CELLS BECAME VISIBLE IN FRONT OF US. I ASKED MY FO TO INFORM THE CTLR WE WOULD HAVE TO MAKE A HARD R TURN. HE DID AND THE CTLR APPROVED IT. SEVERAL MINS LATER I TOLD THE FO TO LET THE CTLR KNOW WE COULD TURN L ON COURSE IN A FEW MI. THE CTLR THEN STATED; ' I DIDN'T THINK YOU WERE GOING TO TURN THAT FAR.' WE THEN SAW TFC COMING AT US ON THE TCASII; AT THE SAME ALT. THE CTLR WAS CONFUSED WHICH WAY TO TURN US AND THEN SAID; 'AT LEAST YOU WON'T HIT.' I OFFERED A 10 DEG L TURN (TOWARD TSTM). HE SAID; 'OK; AND CLB IMMEDIATELY TO FL370 AND PREPARE FOR AN IMMEDIATE DSCNT BACK TO FL350.' WE COMPLIED; AND ADVISED WE COULD ONLY CONTINUE ON PRESENT HDG FOR 1 MORE MI. HE THEN CLRED US TO FL350 AND GAVE PERMISSION TO DEVIATE. THE OTHER TFC BECAME A YELLOW TARGET ON TCASII. HOWEVER; WE NEVER REACHED THE POINT OF RECEIVING AN RA. IT APPEARED THAT THE CTLR HAD A LARGE AREA TO COVER; WITH SEVERAL ACFT DEVIATING. IT WAS OBVIOUS HE DID NOT SEE OUR SIT DEVELOP AND DIDN'T KNOW HOW TO IMMEDIATELY CORRECT THE PROB. ALTHOUGH I THOUGHT I HAD COMMUNICATED OUR PLAN AS SOON AS WE HAD ONE; I PROBABLY SHOULD HAVE CONTINUED TO UPDATE HIM.