C550 FLT CREW ON VISUAL APCH RESPONDS TO TCASII AND CTLR TA'S TO AVOID TFC WHICH FAILED TO ADHERE TO STATED DEP HDG.

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OUR ACFT HAD BEEN CLRED FOR A VISUAL APCH TO TKI BY DFW REGIONAL APCH. WX WAS GOOD VFR. WE WERE APCHING THE ARPT FROM THE NE; TO ENTER A R DOWNWIND LEG FOR LNDG ON RWY 35. THE ARPT WAS IN SIGHT AS WE WERE HANDED OFF TO TKI TWR. TWR ADVISED US THAT WE WERE TO FOLLOW AN ACFT ABOUT 2 MI SW OF THE ARPT ON AN APCH TO RWY 35. WE WERE THEN APPROX 2 MI NE OF THE ENTRY POINT TO THE R DOWNWIND AT AN ALT OF ABOUT 2100 FT MSL (1500 FT AGL). AS WE ACKNOWLEDGED THAT XMISSION; OUR ONBOARD TCASII SYS ISSUED A TA OF 'TFC; TFC.' THE FO CHKED THE TCASII DISPLAY AND ADVISED ME THAT THE TARGET WAS AT OUR 1 O'CLOCK POS AND 100 FT ABOVE OUR ALT. SIMULTANEOUSLY; THE TWR ADVISED US TO LOOK FOR TFC AHEAD AND TO OUR R. WE HAD EASILY SIGHTED THE TFC BY THIS TIME; WHICH WAS CLRLY EBOUND AND DEFINITELY APPEARED TO BE IN A CONFLICTING POS WITH OUR FLT PATH SO I IMMEDIATELY INITIATED A MODERATE R-HAND TURN TOWARDS THE PATTERN UPWIND; IN ORDER TO PASS BEHIND THE TFC. WHILE I DID NOT HAVE VERY MUCH TIME TO LOOK AT THE OTHER ACFT; IT DID NOT APPEAR TO TAKE EVASIVE ACTION OF ANY KIND. AS I WAS STARTING TO ROLL OUT OF THE R TURN IN ORDER TO RE-ENTER THE DOWNWIND; THE TCASII ISSUED AN RA OF 'DSND; DSND.' WE WERE NOW PASSING BEHIND THE TFC AT THEIR 8 O'CLOCK POS; WITH WHAT LOOKED LIKE ABOUT 3/4 MI OF SEPARATION. AS WE WERE NOW CLR OF THE TFC (AND DIVERGING); I DID NOT DSND AS WE WERE NOW IN THE TFC PATTERN AT THE PROPER ALT. AT THIS TIME THE TWR CTLR CALLED THE OTHER ACFT AND SAID SOMETHING LIKE 'I THOUGHT YOU TOLD ME A NW DEP.' AFTER A FEW SECONDS; A FEMALE VOICE REPLIED; 'NE DEP.' I ROLLED OUT ON A HDG APPROPRIATE FOR THE DOWNWIND AND PROCEEDED SBOUND. WE SIGHTED THE TFC ORIGINALLY ASSIGNED BY THE TWR; ON SHORT FINAL; AND FOLLOWED THAT ACFT TO AN UNEVENTFUL LNDG. AFTER CLRING THE RWY; I MENTIONED TO THE TWR CTLR THAT WE WERE CERTAINLY GLAD TO HAVE HAD TCASII ON BOARD; EVEN THOUGH HE HAD MADE A VERY TIMELY ADVISORY ABOUT THE TFC. HE STATED THAT 'WE JUST CHKED THE TAPES AND THEY HAD DEFINITELY REQUESTED A NW DEP (WHICH WOULD HAVE TAKEN THEM AWAY FROM OUR POS). I SUBSEQUENTLY THANKED HIM AGAIN FOR PICKING UP THE CONFLICT AND FOR THE HELPFUL ADVISORY. NO ONE IN OUR ACFT WAS INJURED BY THE MANEUVERING; NOR EVEN APPEARED TO BE ALARMED. THEY DID ASK ABOUT 'THAT R TURN' AND ALSO ASKED WHETHER OUR EQUIP (TCASII) HAD WORKED AS ADVERTISED. THEY SEEMED AT EASE WITH THE SIT. FACTORS CONTRIBUTING TO THE EVENT: 1) THE PLT OF THE OTHER ACFT SIMPLY TURNED THE WRONG WAY AFTER HAVING BEEN CLRED FOR TKOF WITH A NW DEP. 2) MCKINNEY ARPT IS A VERY NICE SATELLITE ARPT FOR THE DALLAS METRO AREA; WITH A FIRST CLASS CTL TWR; INST APCHS AND NO OBSTRUCTIONS. IT IS A POPULAR ARPT FOR STUDENT TRAINING AND FOR BUSINESS TFC NEEDING EFFICIENT ACCESS TO THE DALLAS AREA. CONSEQUENTLY; THERE IS OFTEN A MIX OF TFC IN THE PATTERN INVOLVING HIGH PERFORMANCE ACFT WITH LOW PERFORMANCE ACFT PLTED BY LESS EXPERIENCED PLTS. FACTORS CONTRIBUTING TO THE OUTCOME: 1) GOOD PERFORMANCE BY ONBOARD TCASII. 2) CAREFUL MONITORING OF TFC AND TIMELY ADVISORIES BY MCKINNEY CTLRS. 3) GOOD CREW COORD AND USE OF TCASII/RADIO TO AVOID CONFLICTS.