C310 ENRTE TO HHR WAS CONFUSED WITH RTEING W OF LAX ARPT.

Narrative

I WAS ON A VFR FLT FROM LVK TO HHR; WITH FLT FOLLOWING PROVIDED BY ATC. WHEN I WAS HANDED OFF FROM ZOA TO SCT APCH; THE CTLR ASKED WHAT RTE I WOULD LIKE TO HAWTHORNE. AFTER LOOKING AT THE LA VFR TERMINAL AREA CHART AND SEEING THE VFR TRANSITION RTE W OF LAX; I REQUESTED THAT RTE. I SPECIFICALLY ASKED FOR THE RTE W OF LAX. THE CTLR RESPONDED WITH WHAT I THOUGHT WAS APPROVAL TO FLY THE RTE. WHEN I WAS ABOUT 1 MI OFFSHORE OF MARINA DEL REY; THE CTLR TOLD ME TO SQUAWK 1200; FREQ CHANGE APPROVED (I WAS DSNDING OUT OF 4500 FT AT THE TIME). THIS SEEMED STRANGE; AS I WAS ABOUT TO CROSS THE DEP END OF LAX; AND I THOUGHT I NEEDED TO REMAIN IN CONTACT WITH ATC TO DO THAT. I ASSUMED THAT THERE MUST BE A LULL IN TFC AT LAX THAT ALLOWED HIM TO DROP CONTACT WITH ME. I COMPLETED THE VFR TRANSITION RTE; TURNED E AT THE REFINERY; AND CALLED HAWTHORNE TWR. AFTER LNDG AT HAWTHORNE; I WAS INSTRUCTED TO CALL SCT APCH AND ASK FOR THE SUPVR. IN MY CONVERSATION WITH THE SUPVR; IT BECAME EVIDENT THAT SCT APCH THOUGHT I WAS GOING TO FLY THE SCT SPECIAL FLT RULES RTE OVER LAX; NOT THE SHORELINE RTE W OF LAX. EVIDENTLY; THERE HAD BEEN A MISUNDERSTANDING OR MISCOMMUNICATION BTWN MYSELF AND THE LA APCH CTLR THAT I HAD INITIALLY CONTACTED. THE SUPVR EXPLAINED THAT THE RTE OVER LAX WAS GREATLY PREFERRED; SINCE IT HAD NO EFFECT ON TFC INTO/OUT OF LAX. I EXPRESSED MY AMAZEMENT TO THE SUPVR THAT THE CTLR WOULD CEASE CONTACT WITH ME WHEN I WAS OFFSHORE OF MARINA DEL REY. IF HE WAS EXPECTING ME TO FLY THE SPECIAL FLT RULES RTE OVER LAX; I WAS NOWHERE NEAR THAT RTE; AS HIS RADAR WOULD SHOW. LESSON LEARNED: THE VFR TERMINAL AREA CHART DOESN'T EVEN SHOW THE PREFERRED SPECIAL FLT RULES RTE; EXCEPT IN THE MARGIN. THIS IS JUST ASKING FOR TROUBLE! AT A MINIMUM; THAT RTE SHOULD BE SHOWN CLRLY ON THE CHART. I ALSO SUGGEST THAT THE SHORELINE RTE NOT BE SHOWN; AS ATC REALLY DOESN'T WANT PEOPLE TO FLY THAT RTE AT ALL.