JS32 CREW HAD CLOSE ENCOUNTER WITH PARACHUTE JUMPERS AT AN AIR SHOW AT ZZZ.

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OUR FLT WAS INBOUND TO ZZZ FROM THE SE WHEN THE AIRPORT WAS VISUALLY ACQUIRED. CENTER HANDED US OVER TO ZZZ TWR (A TEMPORARY TWR IN PLACE) WHEN WE WERE APPROX 8 TO 10 MILES OUT. TWR INSTRUCTED US TO PLAN A STRAIGHT IN TO RWY. I DECLINED AS THIS IS A FAIRLY SHORT RWY X AND WOULD HAVE GIVEN US A 5 TO 7 KT TAILWIND. I SUGGESTED A LEFT DOWNWIND ENTRY TO RWY Y. AND THIS WAS GRANTED WITH THE STIPULATION WE RPT 5 MI E OR A 5 MI FINAL. I DID NOT UNDERSTAND THIS TO MEAN WE WERE TO FLY A 5 DME ARC AROUND THE ARPT; BUT THIS IS APPARENTLY WHAT WAS INTENDED AS I TURNED ONTO A LEFT DOWNWIND FOR RWY Y; (APPROX 2 MI S OF THE ARPT.) I HEARD A RADIO CALL SAYING 'GET THAT ACFT OUT OF HERE; HE'S TURNING INTO OUR DROP ZONE.' I IMMEDIATELY STARTED A HARD LEFT TURN (45 DEG BANK ANGLE) TO EXIT THE DROP ZONE AS I COULD NOW SEE ROUGHLY 10 TO 12 PARACHUTISTS AT MY 12 O'CLOCK HIGH POSITION. THE TWR THEN TOLD ME THEY HAD INTENDED I REMAIN AT LEAST 5 MI FROM THE ARPT AT ALL TIMES AND TO RPT A 5 MI FINAL. I ACKNOWLEDGED THIS AND RE-ENTERED THE PATTERN FOR AN UNEVENTFUL APCH AND LANDED ON RWY Y. I BELIEVE THERE WERE SEVERAL FACTORS THAT RESULTED IN THIS 'NEAR MISS' INCIDENT. 1) CENTER NEVER GAVE ANY TYPE OF ADVISORY THAT PARACHUTE JUMPING WAS UNDERWAY AT ZZZ. I NEVER HEARD A '1 MIN PRIOR TO JUMP' CALL OR 'JUMPERS AWAY' CAL. THIS IS IN CONTROLLED AIRSPACE AND SHOULD BE REQUIRED. 2) WHEN I CALLED ZZZ TWR; I WAS NOT INFORMED A JUMP WAS IN PROGRESS SE OF THE ARPT; CLOSE TO OUR POSITION. 3) ADDING TO THE CONFUSION WAS IMPROPER AND POOR PHRASEOLOGY. WE SHOULD HAVE BEEN TOLD TO FLY A SPECIFIC HDG OR TO FLY A 10 DME ARC AROUND THE ARPT TO STAY AWAY FROM THE DROP ZONE. ON TOP OF ALL THIS TWR PERSONNEL LATER TOLD ME THEY DO NOT CTL THE TIME OF THE PARACHUTE OPERATION OR THE AREA IN WHICH THEY LAND. APPARENTLY THE JUMPERS HAVE THEIR OWN BOUNDARIES THAT THEY HAVE DETERMINED WILL BE SAFE FOR EVERYONE. THIS IS OBVIOUSLY NOT WORKING AS ON A SUBSEQUENT TAKEOFF FROM ZZZ; WE HAD 2 JUMPERS CROSS OUR RWY APPROX 300 TO 400 FT ABOVE US JUST AFTER ROTATION. I BELIEVE THE SOLUTION IS TO SUSPEND ALL PARACHUTING ACTIVITY WHEN SCHEDULED AIRLINERS ARE OPERATING WITHIN A 30 NM RADIUS OF THE ARPT. ADDITIONALLY; AIRCREWS FLYING IN AND OUT OF THESE ARPTS SHOULD BE GIVEN A PACKET DESCRIBING ALL ARRIVAL AND DEP PROCEDURES. BETTER COORD BETWEEN ALL PARTIES INVOLVED IS THE KEY TO SAFE OPS.