NMAC BTWN ACFT X AND ACFT Y. CONVERGING COURSE TFC PATTERNS FOR INTERSECTING RWYS.

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I WAS HEADED NBOUND TO FLYING CLOUD ARPT TO DO A TOUCH AND GO LNDG. I RPTED BEING OVER PRIOR LAKE; A NORMAL RPTING POINT ABOUT 8 NM S OF THE ARPT. I WAS INSTRUCTED TO RPT R DOWNWIND FOR RWY 18. OVER THE NEXT 2 OR 3 MINS THERE WAS A CONTINUING DISCUSSION BTWN A KING AIR AND THE TWR CONCERNING WHICH RWY TO USE. THEIR CONVERSATION ENDED WITH A CLRNC FOR THEM TO USE RWY 9R. I HAD NO VISUAL CONTACT WITH THE KING AIR. I WAS WORRIED ABOUT A POSSIBLE CONFLICT WITH THE KING AIR WHICH I ASSUMED TO BE E OF MY POS; SO AFTER A SHORT TIME (APPROX 3 MINS) INBOUND FROM MY INITIAL CALL I ASKED MY PAX; ANOTHER PLT TO RADIO OUR POS TO THE TWR. HE RPTED OUR POS AS OVER VALLEY FAIR ANOTHER PROMINENT LANDMARK APPROX 2 NM FROM FLYING CLOUD ARPT AND ASKED IF WE WOULD BE SWITCHED OVER TO RWY 9R. THE TWR SAID NO THAT WE SHOULD CONTINUE IN A N-EASTERLY DIRECTION AND PASS BEHIND THE KING AIR. SHORTLY AFTER THAT I SAW THE KING AIR TO MY R AND APPROX 50-100 FT ABOVE ME. I AVOIDED THE KING AIR BY A RAPID DSCNT. THE KING AIR PASSED IMMEDIATELY OVER ME. FROM FURTHER CONVERSATION BTWN THE KING AIR AND THE TWR; IT WAS CLR THAT THE KING AIR HAD NOT SEEN ME EARLIER. WE SEEMED TO SEE EACH OTHER AT APPROX THE SAME INSTANT. THE TIME BTWN MY INITIAL CALL TO THE TWR AND THE CLOSE CALL WAS APPROX 3 MINS. THIS COULD HAVE BEEN AVOIDED BY: THE TWR COULD HAVE ADVISED US HOW CLOSE THE TFC WAS TO US (I THINK THAT HE WAS PREOCCUPIED BY HIS CONVERSATION WITH THE KING AIR) OR ADVISED THE KING AIR OF OUR POS. HE COULD HAVE ALSO ANTICIPATED THE POTENTIAL CONFLICT SEVERAL MINS EARLIER AND ASKED US TO VARY OUR COURSE IN ORDER TO HAVE ENOUGH SPACE TO PASS BEHIND THE KING AIR. THE KING AIR COULD HAVE LOOKED FOR US ALSO. HIS ATTITUDE BASED ON HIS COMMENTS BEFORE AND AFTER THE CONFLICT WAS THAT HE OWNED THE AIR AND WE GOT TOO CLOSE TO HIM. I SHOULD HAVE IMMEDIATELY ADVISED THE TWR THAT I DID NOT HAVE VISUAL CONTACT WITH THE KING AIR. WHILE DEPARTING THE CTLR ASKED IF I HAD SEEN THE KING AIR. MY PAX SAID NO AND THERE WAS ONE FURTHER COM. SUPPLEMENTAL INFO FROM ACN 316133: I WAS A PAX BUT WAS RUNNING RADIOS BECAUSE THE PLT WAS NERVOUS ABOUT A TOWERED ARPT; WHICH HE'S NOT USED TO. I ASKED TWR IF WE SHOULD TAKE RWY 9R AND TWR SAID NO. I THOUGHT TWR SAID TO FOLLOW THE KING AIR; WHICH WE DID NOT YET SEE; AND HE EMPHATICALLY SAID 'DO NOT FOLLOW.' AT THIS POINT I SAW THE KING AIR TO MY R AND JUST ABOVE US. I POINTED DOWN; FOR THE PLT TO DSND QUICKLY; WHICH HE DID. THE KING AIR PASSED OVER US 30-50 FT ABOVE. WE HAD NOT SEEN THE KING AIR; WHICH I DON'T THINK HAD ITS LNDG LIGHT ON. TWR HAD NOT ADVISED US OF HOW CLOSE THE KING AIR WAS; NOR DID I HEAR THE KING AIR ADVISE THAT HE HAD US IN SIGHT. WE COULD HAVE AVOIDED THIS BY ASKING TWR FOR POS OF THE KING AIR. I WISH THE TWR WOULD HAVE HAD US TURN E UNTIL HE WAS PAST US.