VFR ACFT ON TRAINING FLT TO CMA RECEIVING FLT FOLLOWING WITH NTD; AND ENTERED OXR CLASS D AIRSPACE WITHOUT CLRNC.

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ON A TRAINING FLT FROM SBA TO CMA WITH FLT FOLLOWING; SBA APCH HANDED US OFF TO POINT MUGU WHO IN TURN TOLD US TO CONTACT CMA TWR. CMA TWR ASKED US TO WIDEN OUT FOR TFC ON BASE TO OXR; INFORMED US WE WERE IN OXR CLASS D AIRSPACE; AND ASKED US IF WE HAD COORD WITH OXR. I HAD NOT CALLED OXR BECAUSE I ASSUMED THAT POINT MUGU HAD TAKEN CARE OF THE COORD WITH OXR. REVIEWING THESE EVENTS AFTER THE FLT; I REALIZED THAT I CAN'T RELY ON THE APCH CTLR TO HANDLE COORD WITH AIRSPACE THAT MAY BE BTWN ME AND MY DEST. I SHOULD HAVE REMAINED CLR OF OXR AND ASKED POINT MUGU IF I WAS CLR; OR CALLED OXR AND COORD WITH THEM MYSELF. IF I HAD NOT HAD FLT FOLLOWING; I WOULD HAVE CALLED OXR. THIS IS A PARTICULARLY DIFFICULT SPOT BECAUSE CMA AND OXR ARE WITHIN A FEW MI OF EACH OTHER; MAKING IT HARD TO CONTACT BOTH FACILITIES IN THE SHORT TIME IT TAKES TO FLY FROM ONE AIRSPACE TO THE OTHER. RIGHT AFTER CMA TOLD US ABOUT THE OXR TFC; THEY HAD A SIMILAR EVENT WITH ANOTHER ACFT APCHING FOR LNDG AT CMA. IT MIGHT BE A GOOD IDEA IF POINT MUGU ADDED A STANDARD REPLY TO APCHING ACFT TO WARN THEM TO REMAIN CLR OF THE ADJACENT AIRSPACE (EITHER CMA OR OXR DEPENDING ON THE ARR ARPT) SO PLTS WILL REALIZE THAT THE FLT FOLLOWING IS NOT PROVIDING ANY COORD.