FLC OF AN MLG ACR ACFT STOPPED DEP CLB IN RESPONSE TO A TCASII RA.

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FLT WAS A SCHEDULED FLT FROM KANSAS CITY TO DETROIT. WX AT KANSAS WAS EXCELLENT -- CLR SKIES WITH UNRESTR VISIBILITY. OUR INITIAL DEP CLRNC WAS TO CLB TO 16000 FT ON A 020 DEG HDG AFTER TKOF FROM RWY 1L. WE WERE TO EXPECT VECTORS TO INTERCEPT THE ROYAL 2 DEP TO KIRKSVILLE THEN DIRECT TO BRADFORD FLT PLAN RTE. SHORTLY AFTER TKOF; DEP CTL ADVISED US THAT VFR TFC WAS AHEAD OF US AT 10500 FT HDG N (OR NW) AT A 2 O'CLOCK POS TO US. WE SCANNED THE AREA BUT WE COULD NOT LOCATE THE ACFT. DEP CTL TOLD US TO LEVEL OFF AT 19000 FT AND THEN GAVE US 040 DEG HDG TO INTERCEPT THE DEP (SEE PLATE). WE WERE STILL LESS THAN 25 MI FROM THE ARPT. WE CONTINUED TO LOOK FOR TFC; BUT COULD NOT SPOT IT. HOWEVER; AS WE NEARED THE TFC ON OUR CONVERGING PATHS; TCASII PICKED UP THE TARGET (WITHIN 6 MI AND PLUS OR MINUS 2700 FT VERTLY) AND DISPLAYED A HOLLOW BLUE DIAMOND. OUR ALT WAS APPROX 8500 FT AT THE TIME. THE FO; WHO WAS FLYING THE ACFT; REDUCED HIS CLB RATE AS A PRECAUTION. THE LATERAL SEPARATION CONTINUED TO LESSEN AS THE PATHS CONVERGED. TCASII THEN CAME ON WITH AN AURAL SIGNAL TO 'MONITOR VERT SPD;' A PREVENTIVE RESOLUTIONARY ADVISORY AND THEN A FURTHER CORRECTIVE RA TO 'REDUCE CLB; REDUCE CLB.' THE FO LEVELED THE PLANE OFF BTWN 9400 FT AND 9500 FT. THE BLUE DIAMOND TARGET INDICATED PLUS 7 (700 FT ABOVE US) AS IT PASSED WITHIN THE 2 MI INNER RING JUST BEHIND US. DEP CTL THEN INDICATED THAT THE TFC WAS PASSING BEHIND US AND GAVE US ZKC FREQ FOR HDOF. AS I COPIED DOWN THE FREQ AND READ IT BACK; I REMARKED THAT 'THAT WAS TOO CLOSE' IN REF TO THE TFC CONFLICT. ZKC ON THE HDOF; ALSO QUESTIONED ME ABOUT THE INCIDENT. I TOLD THEM THAT WE HAD LEVELED OFF WITH AN INDICATION OF TFC ONLY 700 FT ABOVE US. HAD WE CLBED TO 10000 FT VERSUS 9500 FT (LEVELOFF) THERE WAS A POTENTIAL FOR A NEAR MISS INCIDENT. I VERIFIED OUR FINAL ACTIONS WERE TO COMPLY WITH TCASII ADVISORIES. TCASII AS AN AID TO COLLISION AVOIDANCE; PROVIDED TIMELY INFO. WHILE THE CTLR; THOUGH NOT REQUIRED TO PROVIDE SEPARATION FROM VFR ACFT; DID SEE A POSSIBLE HAZARD AND CALLED FOR AN EARLY LEVELOFF. A BETTER VECTORED HDG AWAY FROM THE TFC MIGHT HAVE BEEN A BETTER ALTERNATIVE.