A MO20J PLT CLBS INTO THE CLASS B OF OAK WHEN TOLD TO 'REMAIN OUTSIDE OF CLASS B.'

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THIS IS MY SECOND EXPERIENCE WITH LACK OF CLARITY IN THE FLOW OF NEEDS FROM OAK TWR THROUGH BAY TRACON TO THE PLT. OAK'S CAB FORCES THEM TO ISSUE DEP DATA THROUGH 121.9 (GND CTL) RATHER THAN THE CLRNC DELIVERY MODE MORE COMMON FOR CLASS C ARPTS. ON GND; OAK TWR APPLIES RADAR SVC TO EVERY PLT WHO CALLS FOR TAXI CLRNC INCLUDING THOSE WHO NEITHER NEED NOR DESIRE IT. BOTH OAK TWR AND BAY HAVE TOLD ME; 'YOU'LL BE ON RADAR EVEN IF YOU REFUSE IT!' I APPRECIATE RADAR SO I NEVER QUESTION THAT. BUT BAY MAY BE UNCLR AS TO PLTS' SITS WHEN TAKING HDOFS FROM TWR. HAVING FILED A VFR FLT PLAN (WITH OAK FSS) I CALLED OAK GND AND SPECIFIED DEMING; NM; AS DEST WITH FIRST TRACK OUT THE CORRIDOR AWAY FROM CLASS B AND CLASS C AIRSPACES TO PALMDALE. OAK GND TOLD ME TO EXPECT 080 DEG HDG (RWY 11/29 WAS CLOSED AND ITS TFC BEING DIVERTED TO RWY 27L). NO INSTRUCTIONS WERE GIVEN REGARDING ALT EXCEPT THE BASIC 'REMAIN OUTSIDE CLASS B AIRSPACE.' AFTER TKOF; OAK TWR HANDED ME OFF TO BAY (I BELIEVE ON EITHER 134.5 OR 135.4) AND I RPTED 'ALT THROUGH' AND PROPOSING CLB TO 7500 FT. I WAS MAINTAINING 080 DEG HDG AND UNDERSTOOD CTLR VECTORS WOULD KEEP ME CLR OF SUA. A FEMALE CTLR ACKNOWLEDGED AT ABOUT THE TIME I CLRED CLASS C AND SECTOR G OF CLASS B. IT IS POSSIBLE THE ASSIGNED HDG TOOK ME INTO A CORNER OF SECTOR H; CLASS B; WHICH IS EFFECTIVE 4500-8000 FT. REACHING 3800 FT; A MALE CTLR INTERVENED TELLING ME 'YOU WERE NOT SUPPOSED TO GO ABOVE 3500 FT' AND 'YOU'VE GOT A JET OUT THERE.' I APOLOGIZED FOR ANY ALT PROB BUT TOLD HIM I HAD HEARD NOTHING ABOUT IT (OF COURSE I HAD NOT READ BACK ANY INFO BLOCKED OUT OR OTHERWISE MISSED). HE ORDERED ME TO TURN L AND 'I WANT YOU DOWN TO 3000 FT.' I DID BOTH AND RPTED LEVEL AT 3000 FT; HDG 050 DEGS. NOW THE FEMALE CTLR CAME BACK ON; CLRING ME ON COURSE AND CLB TO 7500 FT! MOST OF THE ATC PEOPLE ARE COMPETENT AND KIND AND I WOULD LIKE TO DO WHATEVER I CAN TO MAKE OUR ROLES SAFE AND EFFICIENT. SPECIFICALLY; ALL CONCERNED NEED TO CONCENTRATE ON THE VITAL ALT ELEMENT OF EACH AND EVERY INSTRUCTION. WHEN OAK TWR HANDS OFF TO BAY; THEY MUST INCLUDE ANY EXACT ALT ISSUED TO AND READ BACK BY THE PLT. IF TWR HAS NOT ISSUED AN ALT LIMIT; BAY WILL NEED TO DO SO WHEN THE PLT MAKES HIS (OR HER) FIRST CALL-UP. OTHERWISE; IT IS 'PLT'S DISCRETION' AND HE (OR SHE) SHOULD NOT BE TAKEN INTO SUA ON VECTORS OR AN ASSIGNED HDG.