HDG AND TRACK DEV LEADS TO A POTENTIAL CONFLICT BTWN AN SR22 AND A FALCON JET OFF THE END OF RWY 19 AT TEB; NJ.

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I WAS LNDG IN FROM THE NW ON VECTORS TO THE VOR/DME-A RWY 19 ARR ON AN IFR FLT PLAN IN VFR WX. I HAD TO COME BACK TO GET THE IAP AS TWR LET ME GO OUT TOO FAR ON THE VECTOR. WAS TOLD TO RPT ARPT IN SIGHT AND DID SO AT THE IAP. TFC WAS QUITE BUSY AND IT WAS DIFFICULT TO GET IN TO THE TWR CTLR. VERY FEW REPLIES TO TWR FROM ANY ACFT; MORE JUST FOLLOWING HIS INSTRUCTIONS. UPON THE SECOND FIX; WAS TOLD TO ENTER A R BASE. TURNED R BASE WITHIN A MIN OR SO FOR RWY 19; AND KNEW A FALCON JET WAS ON BASE ALSO; BUT DID NOT SEE HIM YET. THERE WERE AS MANY AS 9 OTHER PLANES ON MY MAP AS WELL. I WAS WITHIN SECONDS OF TURNING FINAL AND HEARD TWR CLR THE FALCON FOR LNDG; LOOKED TO THE L AND SAW THE FALCON ON FINAL ABOUT 1/4 MI OFF MY L WING. CALLED TWR IMMEDIATELY TO RPT THAT I WAS ABOUT TO TURN FINAL AND TOOK FLAPS TO 50%; FULL PWR AND CLBED. TWR THEN ASKED FOR MY POS BY ASKING 'WHERE ARE YOU?' TOLD HIM I WAS ABOUT TO TURN FINAL AND HAD THE FALCON. I WAS GIVEN AN IMMEDIATE CLB TO 1000 FT AND BY THE TIME I GOT THAT I WAS WELL ABOVE THE FALCON ALREADY GOING THROUGH 800 FT. TOLD TWR I HAD THE FALCON AND THEY WERE CLR OF ME. THEY LANDED UNDER MY PATH. TWR TURNED ME 270 DEGS AND CLRED ME TO LAND WITH A SNAP THAT I WAS CLRED TO LAND AGAIN #2. I NEVER DID GET INSTRUCTIONS TO LAND #2. GND GAVE ME A NUMBER TO CALL ON TAXI. CALLED THEM AND CTLR WANTED TO KNOW WHY I DID NOT STAY ON DOWNWIND UNTIL TWR TOLD ME TO TURN BASE. I EXPLAINED THAT WAS NEVER ON A DOWNWIND FROM THE POS I WAS ENTERING THE PATTERN. THEY GAVE ME [INSTRUCTIONS] TO TURN R BASE FROM MY POS. CTLR DENIED I WAS GIVEN A BASE TURN; AND I APOLOGIZED IF I MISUNDERSTOOD THAT THEY WANTED ME TO FLY PARALLEL WITH THE RWY; MAKE A 180 DEG TURN AND ENTER A R DOWNWIND INSTEAD OF A R BASE. CTLR SIMPLY STATED THAT I NEEDED TO LISTEN MORE CAREFULLY IN THE FUTURE. I ASSURED CTLR I WOULD. I EITHER MISUNDERSTOOD TWR'S INSTRUCTIONS OR WAS GIVEN IMPROPER INSTRUCTIONS. EITHER WAY; TWR WAS NOT AWARE OF MY POS AS HE ASKED 'WHERE ARE YOU?' PREVENTION OF THIS WOULD BE TO HAVE TWR MORE AWARE OF CURRENT POS AND OF COURSE PLTS FOLLOWING INSTRUCTIONS AND LISTENING BETTER; INSTEAD OF ASSUMING THE NEXT POS MOVE. THANKFULLY; I WAS AWARE OF THE FALCON IN THE PATTERN WITH ME AND KNEW WHERE TO LOOK FOR IT.