NMAC BTWN AN ACR MLG AND A C421 ON A HEAVILY TRAVELLED ARR RTE.

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WHILE LEVEL AT 10000 FT; ATC ADVISED US OF TFC AT 12 O'CLOCK 6 MI. I DID NOT SEE THE TFC AT THIS TIME; BUT NOTED THAT THE TCASII SHOWED TFC IN THAT LOCATION AT OUR ALT. MOMENTS LATER TCASII GAVE AN AURAL TA AND A YELLOW CIRCLE VISUAL ALERT. I THEN SAW THE TFC APCHING HEAD ON AT APPROX 3 MI. AS I WAS CONSIDERING THE BEST PLAN OF ACTION; ATC CALLED WITH A MORE URGENT TA (NOW 1-2 MI DISTANT) AND A CLRNC TO TURN L TO A SPECIFIC HDG. DURING THE ATC XMISSIONS I TOLD THE FO I HAD THE TFC IN SIGHT; THE TCASII GAVE AN AURAL 'DSND; DSND;' I DISENGAGED THE AUTOPLT AND STARTED A GENTLE DSCNT FOLLOWED BY A L TURN. TCASII THEN ANNOUNCED 'MONITOR VERT SPD' AS I MANEUVERED THE ACFT SO AS TO REMAIN OUTSIDE THE RED BOUNDARIES ON THE ATTITUDE INDICATOR. I TOLD THE FO TO 'TELL HIM WE ARE DEVIATING FOR AN RA;' REFERRING TO ATC. ATC IMMEDIATELY GAVE US A CLRNC TO 7000 FT. I ESTIMATE OUR ALT AT 9800 FT WHEN WE RECEIVED THE CLRNC. THE TFC PASSED OFF OUR R AT APPROX 200-300 FT. AT ABOUT 300 FT ABOVE US AND TCASII ANNOUNCED 'CLR OF CONFLICT!! THE ACFT WAS A MOSTLY WHITE C421 WHICH I WAS ABLE TO SPOT MORE EASILY BECAUSE THE L WINGTIP LNDG LIGHT WAS ON. OUR SPD REACHED 255 KIAS. SO I REDUCED THE PITCH DOWN TO BLEED THE SPD BELOW 250 BEFORE CONTINUING THE DSCNT TO 7000 FT. WE LATER ASKED FOR AND RECEIVED A TELEPHONE NUMBER FOR BAY APCH. I TALKED WITH AN APCH CTL SUPVR WHEN WE ARRIVED IN OAKLAND AND WAS TOLD THE 421 HAD LEVELED AT 9800 FT THEN STARTED A VERY SHALLOW CLB WHEN THE CTLR FIRST CALLED IT AS TFC FOR US. THE 421 WAS SQUAWKING 1200; NOT TALKING TO ATC; AND CONTINUED A CLB VERY SLOWLY TO 11700 FT OUT A HEAVILY TRAVELLED ARR RTE TO THE BAY AREA. THE SUPVR ALSO STATED THE 421 AFFECTED 2 OTHER ACRS FOLLOWING US. THE SUPVR ALSO STATED THAT OUR DSCNT IN RESPONSE TO THE TCASII RA RESULTED IN NO EFFECT ON TFC SEPARATION. A LATER DEBRIEF OF THE FLT ATTENDANTS REVEALED THEY WERE NOT AWARE OF ANY UNUSUAL MANEUVERING ON OUR ARR TO OAKLAND; AND COULD NOT REMEMBER HEARING THE TCASII AURAL WARNINGS BLARING THROUGH THE COCKPIT DOOR. I FEEL THIS IS A TEXTBOOK EXAMPLE OF HOW TCASII AND ATC ARE SUPPOSED TO FUNCTION IN CONFLICTS LIKE THIS.