A DEP CLBING HS125-800 OVERSHOT ITS TURN DURING A SID DEP AND SUFFERS A POTENTIAL CONFLICT WITH A DSNDING ACFT THAT HAD JUST RELEASED ITS JUMPERS.

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WE WERE DEPARTING ONT TO THE SE ON THE SID; WITH THE ROUTING VIA THE THERMAL TRANSITION. MY FO WAS IN THE L SEAT AND WAS THE PF. WE WERE IN A HAWKER 800. WHILE LONG RANGE NAV WITH GPS WAS AVAILABLE; THE FO HAD ELECTED TO USE PRIMARY VOR NAV FOR THE SID; WITH INTENT TO SWITCH TO LONG RANGE NAV FOR THE REMAINING ENRTE PORTION OF THE FLT. THERE IS A NEARLY 90 DEG L TURN OFF THE SEAL BEACH VOR TO COMPLETE THE THERMAL TRANSITION. AS THE FO WAS APCHING THIS L TURN; I REMINDED HER OF THE UPCOMING TURN AND SHE ACKNOWLEDGED THIS. JUST BEFORE INTERCEPTING THE RADIAL FROM THE SEAL BEACH VOR THE TCASII INDICATED TFC; AND NEARLY SIMULTANEOUSLY WITH THE INITIAL APPEARANCE ON THE SCREEN; IT SOUNDED THE ALARM FOR POTENTIAL CONFLICT. THE FO AND I LOOKED FOR THE TFC AND AT ABOUT THE 1 O'CLOCK POS; WE NOTICED AN ACFT IN A TURN AND AT A SEVERE NOSE DOWN ATTITUDE. THE ACFT APPEARED TO BE ABOUT 1-2 MI AWAY AT MINIMUM; POSSIBLY MORE (THIS WAS A BIT DIFFICULT TO DETERMINE VISUALLY DUE TO THE DIVE THE ACFT WAS IN). THE FO REDIRECTED HER ATTN QUICKLY TO THE NAV DISPLAY AND INITIATED THE L TURN TO INTERCEPT THE SEAL BEACH RADIAL AS PER THE SID. WHILE THE MOMENTARY DISTR DID CAUSE HER TO FLY PAST THE CTRLINE; AT NO TIME DID HER VOR DISPLAY INDICATE MORE THAN 1/2 - 3/4 DOT DEFLECTION; THUS INDICATING THAT WHILE WE WERE A BIT S OF THE CTRLINE; WE WERE CERTAINLY STILL WITHIN PROTECTED AIRSPACE. AT ABOUT THAT TIME; ZLA ASKED US IF WE WERE IN THE L TURN. I RESPONDED AFFIRMATIVE AND SAID I SAW TFC THAT APPEARED TO BE DOING AEROBATICS. CTR TOLD ME IT WAS A PARACHUTE ACFT AND THAT HE INDICATED WE WERE 3 MI S OF COURSE. I INDICATED THAT OUR DISPLAY WOULD INDICATE WE WERE 'NEARLY RIGHT ON' COURSE. CTR DID NOT INDICATE THE LEVEL OF ALERT HE EXPERIENCED; BUT DIDN'T SEEM TO INDICATE A SIGNIFICANT CONFLICT. THE CONCERN IS THAT HE MAY FEEL WE WERE FURTHER S OF COURSE THAN OUR VOR DISPLAY WOULD HAVE INDICATED FOR US. WHILE WE DID EXTEND JUST A BIT S OF THE CTRLINE; CERTAINLY WE DID NOT VIOLATE THE AIRSPACE AS PER OUR INDICATIONS. AS IS TYPICAL FOR TCASII; IT CAN SOMETIMES PRESENT A SIGNIFICANT DISTR THAT LEADS TO CREW INATTN BRIEFLY TO OTHER TASKS. ANOTHER CONCERN IS WHY THE OTHER ACFT WAS PERMITTED TO DISCHARGE JUMPERS SO CLOSE TO THE AIRWAY. IT WAS SURELY A RECREATIONAL FLT AS THERE WAS NO APPARENT FIRE AND NO NOTAM FOR EMER JUMPING IN THE AREA. WHILE I HAVE ENCOURAGED THE FO TO UTILIZE THE VERY ACCURATE LONG RANGE GPS NAV MODE IN THE FUTURE; AND TO LEAD TURNS SOONER; I ASSERT THAT WE DID NOT VIOLATE AIRSPACE PER OUR INDICATIONS ON THE VOR CDI INDICATIONS. RECREATIONAL PARACHUTE JUMPING SHOULD ALSO NOT BE PERMITTED SO CLOSE TO AIRWAYS OCCUPIED BY HIGH SPD JET TFC.