A PA46 MALIBU CPR PLT IS TOLD TO MAKE A GAR BY CTLR WHEN HE COMES IN CLOSE PROX OF A BE35 ON FINAL APCH TO RWY 16 AT EUG; OR.

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I WAS ON A 340 DEG VECTOR; WHICH IS DOWNWIND; L TFC TO RWY 16 EUG; AT 5000 FT. APCH CALLED 'TFC; 11 O'CLOCK POS; 3.6 MI AT 2500 FT; A BONANZA.' I ACKNOWLEDGED; AND SHORTLY THEREAFTER SAW AN ACFT BELOW ME; 10-11 O'CLOCK POS ON EXTENDED FINAL TO RWY 16. I RPTED TFC IN SIGHT; AND WAS 'CLRED VISUAL APCH; RWY 16; BEHIND THE BONANZA' BY CASCADE APCH. I MAINTAINED CONTACT WITH THE TFC; BEGAN TO DSND OUT OF 5000 FT CONTINUING THE DOWNWIND UNTIL THE TFC WAS ABOUT 8 O'CLOCK POS. I CONTINUED THE DSCNT AND TURNED BASE TO RWY 16. I SQUARED THE BASE TO FINAL TURN TO MAINTAIN SEPARATION FROM THE LEADING TFC. WHEN I WAS ABOUT TO LEVEL OUT ON FINAL; TWR CALLED 'DO YOU HAVE THE BONANZA IN SIGHT; DISREGARD; IMMEDIATE L TURN TO 090 DEGS; BONANZA XXX IMMEDIATE R TURN TO (SOMETHING).' RATHER THAN LEVELING THE BANK; I INCREASED BANK ANGLE AND CONTINUED THE TURN THROUGH 160 DEGS TO 090 DEGS AND TERMINATED THE DSCNT. ONCE ON 090 DEG HDG I CLBED SLIGHTLY TO MAYBE 2000 FT MSL AND WAS VECTORED BY TWR TO 340 DEG HDG; AND CLRED FOR APCH AND CLRED TO LAND. LNDG WAS UNEVENTFUL. THE OTHER ACFT (THE BONANZA WAS NEVER IN SIGHT; AND I HAVE NO INFO ON THAT ACFT'S POS OR ACTIONS BEYOND WHAT I WAS TOLD BY ATC; OR DERIVED FROM PARTIAL RADIO XMISSIONS BTWN APCH (119.6) AND TWR (118.9) FREQS. MY ONLY COMMENT IS THAT A COMMON WORDING THAT WOULD HAVE ALERTED ME TO THE PRESENCE OF A 3RD ACFT ON APCH IS 'CLRED VISUAL APCH; THIRD BEHIND THE BONANZA.' ULTIMATELY; THE ATC SYS WORKED WELL BECAUSE NO DAMAGE OR INJURIES RESULTED.