TRACON CTLR ALLOWS B737 TO DEP FROM BAY TRACON DELEGATED AIRSPACE INTO ZOA AIRSPACE WITHOUT COMPLETING A RADAR HDOF. TRACON UNABLE TO CONTACT NORAC ACFT SINCE FLT WAS STILL ON TWR FREQ.

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ACFT #1 DEPARTED SJC ON RWY 12; SOUTHLAND 8 DEP. ACFT #1 CLBED OUT NORMALLY; BUT ZOA DID NOT TAKE THE HDOF. MANUAL HDOF WAS INITIATED AS THE ACFT WAS CLBING THROUGH 13000 FT; ENTERING ZOA AIRSPACE. WHEN ZOA WAS CALLED WITH THE HDOF; THE CTLR INDICATED HE HAD BEEN TRYING TO CALL US TO STOP THE ACFT AT AN INTERIM ALT. HE ACCEPTED THE HDOF; AND WE ISSUED THE ALT AND FREQ CHANGE. ACFT #1 DID NOT RESPOND; EVEN AFTER NUMEROUS XMISSIONS. WE NOTIFIED ZOA OF THIS. ACFT #1 SUBSEQUENTLY RPTED LEVEL AT FL230 ON MY FREQ. WE AGAIN TOLD ACFT #1 TO CALL ZOA. HE ACKNOWLEDGED. WE SHOULD HAVE INITIATED VERBAL HDOF SOONER; AND STOPPED THE CLB IF NO RESPONSE FROM ZOA. WE DID NOT HEAR ZOA CALLING US. ZOA COULD HAVE TAKEN THE HDOF; THEN STOPPED THE ACFT AT AN APPROPRIATE ALT. THE ALT ZOA WANTED US TO ISSUE WAS IN ZOA AIRSPACE. THE CREW OF ACFT #1 WAS APPARENTLY PREOCCUPIED WITH OTHER DUTIES AND DID NOT HEAR THE CALLS MADE TO HIM. SUPPLEMENTAL INFO FROM ACN 423216: ON PUSHBACK AT SJC DEP RWY WAS CHANGED FROM RWY 30L TO RWY 12R AND DEP SID WAS CHANGED FROM LOUPE TO MOONY ONE FL230. TOOK OFF AND FLEW MOONY ONE AS PUBLISHED; APCHING OUR ALT CLRNC TO FL230 ESTABLISHED INBOUND TO PXN ON THE 288 DEG RADIAL I REALIZED WE WERE STILL ON SJC TWR (124.0) FREQ. I SWITCHED TO BAY DEP 120.1 FREQ AND CHKED IN. BAY DEP SWITCHED US TO ZOA. I DO NOT BELIEVE SJC TWR HAD PREVIOUSLY DIRECTED US TO SWITCH TO BAY DEP. MY RECOLLECTION OF THE COM ON THE TWR DURING THE INITIAL PORTION OF OUR CLB WAS THAT IT SOUNDED LIKE DEP COM. THIS MAY HAVE CONTRIBUTED TO OUR FAILURE TO REALIZE WE WERE STILL ON TWR FREQ WHEN WE EXPECTED TO BE SWITCHED TO DEP. THE FACT THAT WE WERE STILL ON TWR FREQ WAS REALIZED AS WE APCHED OUR ALT CLRNC AND WANTED TO CONTINUE THE CLB. WE DID NOT EXPERIENCE ANY TA'S. I BELIEVE THIS COM PROB COULD HAVE BEEN PREVENTED IN ANY OF 3 WAYS: 1) TWR DIRECTS SWITCH TO DEP. 2) AIR CREW CATCH ANY OMISSION OF DIRECTED SWITCH AND TAKE ACTION. 3) IF DEP DOES NOT HAVE COM WITH AN ACFT ON DEP THEY SHOULD GO BACK TO TWR TO SORT OUT THE PROB.