PVT PLT OF SMA ACFT INADVERTENTLY PENETRATED A TCA DUE TO A MISUNDERSTANDING OF ATC INSTRUCTIONS.

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I WAS CLRED FOR THE SHORELINE RTE TO TRANSITION LAX. AT THE TIME I WAS ALMOST 1/2 WAY THROUGH THE CTLR CANCELLED THE RTE CLRNC AND SAID TO USE LA VFR FLT RULES AND SQUAWK 1200. MY INTERPRETATION OF VFR FLT IN LA BASIN IS TO GET OUT OF THE TCA. I LOOK AT THE LA TCA CHART AND HAD TO TURN W TO GET 11 NM OUT OF THE TCA TO GET UNDER THE TCA IN ORDER TO GO N OR GO BACK TO LONG BEACH FOR THE HOLLYWOOD PARK RTE AT 8500 MSL IN RTE TO VAN NUYS. THERE WAS A BROKEN LAYER ON TOP SO THE CHOICE WAS MADE TO GET OUT OF THE TCA BY DROPPING 1500 FT OVER THE OCEAN OUT 11 NM THEN N TO MALIBU BEACH UNDER THE TCA. IN DISCUSSING THIS WITH ANOTHER PLT LATER; I WAS TOLD THAT THE CTLR WAS TELLING ME THAT I WAS TO GO R TO OVER THE COAST LINE TRANSITION DIRECTLY OVER LAX AT 4500 AND SQUAWK 1201. MY MISUNDERSTANDING WAS THAT I DIDN'T THINK THE CTLR WAS TALKING ABOUT A FLT 'RTE' BUT WAS TALKING ABOUT OPERATING IN VFR NON RADAR SVC AREAS AROUND THE WHOLE LA BASIN. I KNEW OF THE OTHER RTES BUT I THINK MY CONFUSION WOULD BE LESS IF THE PROC IS LABELED MORE LIKE A RTE RATHER THAN A WAY OF FLYING. IT IS TOO EASY TO BE FLYING VFR FLT FOLLOWING AND THEN BE CANCELLED TO 'SVCS TERMINATED; SQUAWK 1200.' I'M THINKING THIS IS WHAT HAPPENED TO ME AND TO LEAVE THE TCA. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO. RPTR DID NOT FURNISH ANY NEW INFO REGARDING THIS MATTER; INCLUDING ANY CONTACT BY THE FAA.