AN ACR FLC MAKING AN APCH TO RWY 9L ENCOUNTERS A SINGLE ENG ACFT MAKING AN APCH TO RWY 9R AND AVOIDS IT BY HOLDING HEADING AND ALT ON THE BASE LEG UNTIL SAFE TO TURN BEHIND AND ABOVE IT. FLL TWR; MIA TWR AND MIA APCH CTL APPARENTLY HAVE A LOA IN WHICH THE APCH CTL POS FOR RWY 9L AND RWY 9R AT FLL USE DIFFERENT FREQS FOR PARALLEL TFC.

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DOWNWIND RWY 9L FLL; APCH CTLR CLRS US TO 2000 FT. RECLRS US TO 2500 FT FOR TFC. BASE RWY 9L FLL; APCH CTLR CLRS US BASE TURN AT 2500 FT; POINTS OUT TFC 9 O'CLOCK 1 MI. I RESPOND 'NO JOY.' I MENTION RWY 9L AND ACR B737 IN SIGHT. CTLR PAUSE THEN (JUST ABOUT TO CROSS EXTENDED RWY 9L CTRLINE) CLRS US FOR A VISUAL. FO WHO IS FLYING SEES A SINGLE ENG PROP AT 12 O'CLOCK AT SAME TIME TCASII TA ALERTS US. TARGET IS 700 FT BELOW WITH DOWN ARROW. FO IS NOT SURE WHAT TARGET IS DOING; ELECTS TO KEEP IT IN SIGHT BY CONTINUING TO FLY BASE. (THIS ACFT WAS NOT POINTED OUT TO US AT ANY TIME; BUT APPEARED TO BE ON A VISUAL FINAL FOR RWY 9R). THIS ACTION CAUSES US TO FLY ACROSS FINAL FOR RWY 9R. WHEN THE CAPT ACQUIRED TARGET VISUALLY; CAPT COMMANDED A HARD L TURN TO INTERCEPT RWY 9L FINAL. THE TARGET ACFT WAS EASILY AVOIDED AND AN UNEVENTFUL LNDG FOLLOWED. BY GOOD 'SEE AND AVOID' BY THE FO AND WITH TCASII TO CONFIRM I BELIEVE A VERY SIGNIFICANT EVENT WAS AVOIDED. IT WAS APPARENT THAT APCH CTLR HAD NO KNOWLEDGE OF OUR TARGET; BUT WERE CONTINUOUSLY ADVISED BY US OF THE CONFLICT AND OUR ACTIONS. ON THE GND (IN ACR OPS FLL) CAPT PHONED BOTH FAA TWR AND APCH CTL TO INQUIRE AND FOUND THAT A LOA (ATC TYPE) EXISTS THAT DEALS WITH WHO IS RESPONSIBLE FOR TFC CTL ON EACH RWY (9L AND 9R). THIS AGREEMENT MAY HAVE A FLAW WHEREBY CTL RESPONSIBILITIES BECOME QUESTIONABLE AND SHOULD BE REVIEWED BY PROPER (NO CONFLICT OF INTEREST) AUTHS. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR SAID THAT HE WAS ON APCH TO RWY 9L WHEN THE OTHER ACFT WAS SIGHTED. HE FLEW BEYOND HIS TURN TO FINAL TO INSURE ADEQUATE SEPARATION. THE FLC RPTED THE OTHER ACFT TO THE APCH CTLR WHO WAS UNAWARE OF IT. THE RPTR SAID THAT HE WAS CURIOS ABOUT HOW THE CTLR COULD NOT KNOW ABOUT THE ACFT WHEN HE HAD RADAR. THE RPTR SAID THAT THE CAPT TALKED TO BOTH THE TWR AND APCH CTL SUPVRS AND THE TWR SUPVR APPARENTLY APOLOGIZED AND BOTH SUPVRS REFERRED TO A LOA BTWN FLL TWR; MIA TWR AND MIA APCH CTL THAT ALLOWS THE USE OF 2 DIFFERENT FREQS FOR THE APCHS INTO RWYS 9L AND 9R AT FLL. THE RPTR FEELS THAT THIS IS UNSAFE BECAUSE IT DOES NOT ALLOW A PARTY LINE TO BE AVAILABLE TO THE PLTS AND REDUCES THEIR POTENTIAL SITUATIONAL AWARENESS. THE RPTR SAID THAT HE HAS TALKED TO SEVERAL OTHER PLTS AT HIS COMPANY WHO SAID THAT THEY HAVE HAD SIMILAR EXPERIENCES ON APCHS AT FLL. HE HAS TOLD THEM THAT THEY SHOULD SEND RPTS TO ASRS.