PENETRATED THE TCA WHILE UNDER RADAR SURVEILLANCE.

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I ENTERED THE TCA AT STL WHILE UNDER FLT FOLLOWING SURVEILLANCE ON 6/THU/88. APPROX 40 MI E OF THE STL VOR; FLT FOLLOWING TERMINATED AND I WAS INSTRUCTED TO SQUAWK 1200 AND CONTACT STL APCH. THE STL CTLR INFORMED ME THAT SHE WAS TOO BUSY TO HANDLE ME; BUT MIGHT BE BACK TO ME IN ABOUT 15 MINS; THEN GAVE ME A FREQ FOR ANOTHER CTLR WHO ALSO INFORMED ME HE WAS TOO BUSY. THE VIS WAS NOT GOOD; 5 OR 6 MI; AND I HAD EXPERIENCED STRONG HEADWINDS AT 8500' EARLIER ON THAT FLT; SO I CONTACTED KC CENTER AND INFORMED THE CTLR OF MY LOCATION; ALT; DEST AND THAT STL WAS TOO BUSY TO HANDLE ME. THE CTLR ASSIGNED ME A TRANSPONDER CODE (NOT 1200) AND ASKED ALT. I INFORMED HIM THAT I WAS AT 6500'; BUT WOULD ACCEPT ANY ALT HE CHOSE. I WAS INFORMED THAT I WAS UNDER RADAR SURVEILLANCE BUT RECEIVED NO FURTHER COMS FROM KC CENTER UNTIL I CALLED THEM WHEN I COULD SEE THE CITY OF ST LOUIS. THE CTLR SEEMED TO EXPERIENCE DIFFICULTY IN RECEIVING MY XMISSION; HOWEVER; I TOLD HIM MORE THAN ONE TIME THAT I COULD SEE ST LOUIS AND DID NOT WANT TO ENTER THE TCA ILLEGALLY. THE CTLR AGAIN ASKED ME TO SAY ALT (THE ACFT HAD A WORKING MODE C) AND THEN INSTRUCTED ME TO CLB TO 8500' SAYING THAT HE WOULD CALL STL APCH TO DETERMINE MY LOCATION. HIS NEXT XMISSION INFORMED ME THAT I WAS ON THE EDGE OF THE TCA APCH AND THAT I SHOULD CLB TO 8500' AND TAKE A S WESTERLY HDG. I COMPLIED AND KC CENTER PROVIDED RADAR SVC TO MY DEST.