NMAC BTWN A BEECH 90 IN CLASS C AIRSPACE WITHOUT CLRNC AND A PIPER SENECA PASSING 300 FT OVER THE TOP OF THE C90.

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I WAS ASKED TO FLY THE LEG -- WHEN THE OWNER RETURNED FROM LUNCH; HE WAS NOT PREPARED TO FLY. I DID NOT CHK THE ADJACENT AIRSPACE LATERAL LIMITS; BELIEVING I COULD AVOID THE BRIZE-NORTON EASTERN BOUNDARY AFTER DEPARTING EGTK RWY 20; BY A SOUTHERLY HDG. AFTER TKOF; I WAS CLBING AND SCANNING FOR TFC. THE FREQ WAS CONGESTED AS WAS THE AIRSPACE. I WAS CHKING THE VFR CHART FOR THE BOUNDARY OF BRIZE-NORTON CTL ZONE; WHILE IN THE CLB. I HAD SEVERAL TARGETS ON THE TCAD; THEY WERE BEHIND ME. I CONTINUED TO REVIEW THE CHART FOR MY POS RELATIVE TO BRIZE AIRSPACE AND WAS ATTEMPTING TO CONTACT BRIZE RADAR. WHEN I LOOKED UP; THE SENECA WAS PASSING OVERHEAD ABOUT 250-300 FT ABOVE. I DON'T THINK HE SAW ME AS HE WAS IN LEVEL FLT AND NOT MANEUVERING. JUST AFTERWARDS; I WAS FINALLY ABLE TO CONTACT BRIZE; THE FREQ WAS VERY BUSY. I WAS ADVISED THAT I WAS ALREADY IN THE CTL ZONE. I WAS THEN GIVEN RADAR INFO AND CLRED TO PROCEED ON COURSE AFTER A FEW RADAR VECTORS FOR TFC. THE PROB AROSE BECAUSE I TOOK OFF WITHOUT BEING SURE OF THE EASTERN LATERAL LIMIT OF THE BRIZE-NORTON AIRSPACE. I THOUGHT I COULD REMAIN CLR BY ROUTING DUE S; BUT THAT WAS NOT THE CASE. AFTER TKOF; I BECAME TOO OCCUPIED WITH NAV AND FAILED TO SCAN ADEQUATELY FOR TFC. THEN FAILED TO REMAIN CLR OF THE AIRSPACE. IN ORDER TO AVOID FUTURE PROBS; I SHOULD ALWAYS REVIEW AIRSPACE FIRST AND PLAN A RTE TO KEEP ME CLR PRIOR TO TKOF. THEN FULL ATTN CAN BE ALLOWED FOR TFC SCANNING.