INADVERTENT TCA PENETRATION AT LGA BY CORPORATE HELICOPTER.

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ON DEP FROM 6N4 E 60 STREET HELIPORT I STARTED A CLBING L TURN. THE CP CALLED LGA TCA FOR A TCA CLRNC. WE DID NOT GET A REPLY AFTER A NUMBER OF CALLS; WE WERE TOLD THAT TCA WAS BUSY. WE MADE OUR REQUEST AND STARTED INTO A L TURN AT THE NORTHERN BOUNDARY OF THE EXCLUSION AFTER COMPLETING APPROX A 90 DEG L TURN AT THE N TIP OF ROOSEVELT ISLAND. THE CTLR CAME BACK AND SAID WE ENTERED TCA WITHOUT CLRNC AND TO SQUAWK XXXX AND PROCEED AS REQUESTED. I THEN COMPLETED MY L TURN AND CLBED TO 1500 TO PROCEED OVER THE TOP OF LGA. I AM SURE THAT AT NO TIME DID I LEAVE THE BOUNDARY OF THE EXCLUSION UNTIL I WAS GIVEN A CLRNC TO DO SO AS SHOWN ON NY HELI RTE MAP. SUPPLEMENTAL INFO FROM ACN 202801: ALL REF TO LANDMARKS CAN BE FOUND ON THE NEW YORK HELI RTE CHART. WE DEPARTED 6NY (60TH STREET HELIPORT) ENRTE TO OUR CORPORATE HEADQUARTERS NEAR BDR. MY FIRST CALL TO TWR/TCA WAS OVER ROOSEVELT ISLAND. NO REPLY FROM LGA. SECOND CALL AS WE TURNED N IN THE EAST RIVER EXCLUSION AT BIG ALICE CLBING. NO REPLY FROM LGA. THIRD CALL TO TWR/TCA AS WE APCHED THE N TIP OF ROOSEVELT ISLAND WAS ANSWERED BY TWR/TCA WITH 'STANDBY'. THE CAPT; FLYING CONTINUED N INTO THE TCA. I QUESTIONED TCA AS TO HOW WE WERE SUPPOSED TO KNOW WHAT WAS GOING ON SEVERAL TIMES SINCE SHE NEXT SAID THAT SHE HAD BEEN ON ANOTHER LINE. CAPT STARTED A L 270 DEG TURN AS THE TWR/TCA CTLR GAVE US A TRANSPONDER SQUAWK; SAID THAT WE WERE IN THE TCA WITHOUT AUTHORIZATION; CLB TO 1500 FT; CLRED AS REQUESTED. I HAD ASKED FOR OVERHEAD NEBOUND. CAPT CONTINUED TURN AND WE PROCEEDED TOWARD LGA. TWR/TCA SAID 'RADAR CONTACT; I SHOW YOU N OF THE N TIP.'