NMAC AVERTED WHEN APCH CTLR AT L30 ADVISES CLBING B757 OF POP-UP TFC; THE RPTR'S C310; AT 12 O'CLOCK POS AT 10500 FT; 33 NM S OF LAS; NV.

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FLT FROM CASA GRANDE; AZ; TO LAS; NV; LNDG AT HND; FLT FOLLOWING WITH ZLA. ABOUT 36 MI S OF LAS VOR; ZLA ADVISED THAT RADAR SVC AND FLT FOLLOWING WERE CANCELED; SQUAWK 1200 AND CALL LAS APCH CTL. I CALLED LAS. THEY ADVISED THEY WERE VERY BUSY AND WOULD TRY TO GET BACK TO ME. VERY SHORTLY THEREAFTER; THEY EXCITEDLY CALLED AN ACR FLT TO TELL HIM HE HAD VFR TFC DIRECTLY AHEAD OF HIM THAT JUST POPPED UP ON THEIR RADAR. HE TOLD THEM THAT HE HAD A TCASII WARNING AND HAD STOPPED HIS CLB. WITHOUT THE TCASII WARNING; I THINK HE WOULD HAVE HIT US. SHORTLY AFTER THAT; WE WERE CLRED TO ENTER LAS CLASS B AIRSPACE AND WERE GIVEN A XPONDER CODE. DSCNT AND LNDG AT HENDERSON WERE ROUTINE. I REALLY DON'T KNOW WHAT TO SAY ABOUT A POSSIBLE REMEDY. I WAS OUTSIDE CLASS B AIRSPACE AT THE PROPER ALT. ACR WAS FOLLOWING HIS ASSIGNED CLRNC AND LAS APCH SAID WE HAD JUST POPPED UP ON THEIR RADAR. IF ZLA HAD GIVEN US A POSITIVE HDOF TO LAS APCH; I DON'T THINK ANY OF THIS WOULD HAVE HAPPENED. IT SEEMS TO BE A COMMON PRACTICE THAT WHEN ATC GETS BUSY AND THEY ARE NEEDED MOST; THEY SIMPLY SAY GOOD-BYE.