A CESSNA CITATION 560 FLC RECEIVED A TCASII RA NEAR THE SPA VOR.

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TALKING TO NEW YORK APCH ON DSCNT TO NEW YORK METRO AREA; I WAS SURPRISED AT THE LATE CALL ON AN AIRLINE TFC L TO R; 500 FT ABOVE; THAT WE WERE MONITORING BOTH VISUALLY AND ON THE TCASII. AFTER ADVISING US TO REMAIN CLR OF CLASS B AIRSPACE UNTIL CLRED; WE GOT A HDOF TO A BUSY FREQ JUST A COUPLE OF MI OUTSIDE THE OUTER RING OF THE CLASS B AIRSPACE. TRYING TO GET A WORD IN EDGEWISE; WE CONTINUED OUR DSCNT TO 2500 FT TO GET BELOW THE AIRSPACE; AND SUDDENLY; AT ABOUT 3300 FT; WE GOT AN RA TO DSND. THE COPLT; WHO WAS FLYING THE AIRPLANE FROM THE L SEAT WAS SOMEWHAT HESITANT AT HIS REACTION TO THE RA AND WAS TRYING TO ACQUIRE THE ACFT VISUALLY. AFTER 2 OR 3 EXTRA SECONDS; REQUIRED FOR NORMAL TCASII RESPONSE AND WITH MY INTERVENTION; WE FOLLOWED THE RA AND DSNDED; AVOIDING (ON DISPLAY) THE OTHER ACFT BY 100-200 FT VERTLY; NEVER HAVING HAD A VISUAL CONTACT. I FINALLY WAS ABLE TO GET THROUGH ON THE FREQ AND WAS ASSIGNED ANOTHER FREQ. AS SOON AS IT WAS DIALED; I HEARD THE PLT OF THE OTHER ACFT QUESTIONING THE OCCURRENCE. THE CTLR'S RESPONSE WAS THAT THE CITATION; NAMELY US; WAS NOT TALKING TO ANYONE. NOT CORRECT! I THINK THAT IFR CLRNC MIGHT HAVE PREVENTED IT; OR PERHAPS; AN EARLIER DSCNT. A QUICKER RESPONSE BY THE PF; TO TCASII COMMANDS; INSTEAD OF TRYING TO VISUALLY LOCATE THE TFC WOULD HAVE INCREASED THE MARGINS. TCASII SAVED THE DAY! I ALSO THINK THAT BETTER SECTORING COULD HELP AVOID SUCH OCCURRENCES. IT ALWAYS SEEMS THAT THE CTLR THAT CLRS ONE INTO CLASS B AIRSPACE; 'OWNS' ONLY A COUPLE OF MI OUTSIDE THE OUTER RING. NOT GETTING THROUGH; OR NOT GETTING CLRED IN THAT PRECIOUS LITTLE TIME RESULTS IN UNPREDICTABLE (FOR THE CTLR) FLT PATH; AND TIGHT MANEUVERING; INCREASING THE POSSIBILITY OF CONFLICTS.