PLT DEPARTED ARPT UNDER FLOOR OF TCA AND PENETRATED WITHOUT CLRNC.

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WE WERE AT MEIGS ARPT; CHICAGO; IL AND GOING VFR TO GRAND RAPIDS; MI. I OBTAINED THIS INFO FROM ATIS; 127.35. CALLED GND TO GET CLRNC AND TAXI INSTRUCTIONS. GND CTL DIDN'T ANSWER; SO I CALLED THE TWR FREQ AND GOT A RESPONSE. AFTER TELLING TWR I WANTED TO DEPART VFR; I WAS INSTRUCTED TO TAXI TO RWY 36. AFTER THE RUN-UP; I CALLED THE TWR AND REQUESTED DEP INSTRUCTIONS. THE TWR WANTED TO KNOW WHAT HDG I WANTED. MY RESPONSE WAS 075 DEGS AND I WAS GOING DIRECT TO PULLMAN VOR. THE TWR CLRED ME FOR TKOF ON RWY 36; WITH A RIGHT TURN TO 075 DEGS; WITH NO COMMENT ON ALT. I STAYED WITH THE TWR FREQ EXPECTING TO BE TURNED OVER CHICAGO APCH 118.4 ON VFR ADVISORIES ON 126.8. MEIGS TWR CALLED ME AFTER APPROX 3 MINS AND REQUESTED I CALL ORD APCH ON 118.4. THIS I DID AND ORD APCH ADVISED I HAD PENETRATED THE BOTTOM OF THE TCA. MY RESPONSE WAS; I HAD REMAINED WITH MEIGS TWR WAITING FOR A TURNOVER AND THAT MEIGS HAD NOT GIVEN ME AN ALT LIMIT. ORD APCH RESPONDED BY STATING THEM WAS NO OTHER TFC AND THAT MEIGS TWR DID NOT HAVE ANY AUTHORITY OVER THE TCA. END OF CONVERSATION. MY MISTAKE; I GUESS; WAS NOT REQUESTING MEIGS TWR TO TURN ME OVER TO ORD APCH RIGHT AFTER TURNING ONTO THE HDG OF 075 DEGS. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING: PLT ACCEPTS RESPONSIBILITY ALTHOUGH STILL NOT SURE HE PENETRATED TCA FLOOR. FEELS ATC COULD BE MORE COOPERATIVE AND ASSIST IN TIMELY HDOF AND REMINDER OF TCA PROX. PLT DID HAVE COMMERCIAL TCA CHART ABOARD.