LOSS OF SEPARATION AT 11000 FT BTWN CLBING B737 AND A BRASILIA ON FREQ WITH FLL DEP CTL AND ZMA CTLR 30 MI NW OF FLL; FL.

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THERE WERE NUMEROUS RAIN SHOWERS AND TSTMS IN THE S AND CENTRAL FLORIDA AREAS AND ON AR RTES OVERWATER. ALL S FLORIDA TFC WERE BEING RTED INLAND OVER FLORIDA CREATING A TFC FLOW PROB. WE WERE CTLED INITIALLY BY FLL DEP; ON A NW COURSE AND CLRED FROM 5000 FT TO 11000 FT. WE WERE ADVISED OF BRASILIA TFC AT 2 O'CLOCK POS ABOVE US AND CLBING TO 10000 FT. WE RPTED THE BRASILIA IN SIGHT AND CONTINUED OUR CLB ABOVE HIM TO 11000 FT. WE LEVELED WITH THE BRASILIA IN SIGHT. WITHIN A FEW MINS WE WERE GIVEN A TURN TO A 320 DEG HDG AND A FREQ CHANGE TO ZMA. I TOLD THE CAPT THAT THIS DID NOT LOOK GOOD BECAUSE THE BRASILIA DID NOT SEEM TO BE LEVELING. HE CHANGED FREQS TO ZMA WHERE THERE WAS VERY HVY RADIO TFC. AS HE WAS WAITING TO CHK IN ZMA THEY CALLED US IN THE BLIND TO TURN TO 270 DEG HDG AND AN IMMEDIATE CLB WITH NO ASSOCIATED ALT. I TURNED AND STARTED A CLB; AT THE SAME TIME WE RECEIVED A TCASII RA TELLING US TO CLB. AS WE CLBED THROUGH 12000 FT; I TOLD THE CAPT THAT WE HAD NOT BEEN GIVEN A NEW ALT YET. HE QUERIED ZMA AND THEY ASSIGNED US 16000 FT THIS WAS THE FIRST NEW ALT WE HAD RECEIVED SINCE 11000 FT. TO OUR KNOWLEDGE WE NEVER GOT A NEW ALT UNTIL THAT POINT AND WE NEVER RESPONDED TO ANY ALT CALL. EITHER FLL DEP NEVER GAVE US A NEW CLRNC OR IT WAS BLOCKED AND WE NEVER GOT IT.