A GA AA-5A CHEETAH PERFORMS AN UNAUTH TKOF FROM RWY 35 AT HOU. IN THE PROCESS THE ACFT CREATES A POTENTIAL CONFLICT WITH A DEP B737 ON RWY 30L. BOTH ACFT TURN AWAY TO AVOID EACH OTHER.

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OUR FLT HOUSTON DIRECT HARLINGEN WAS CLRED FOR TKOF ON RWY 30L BY HOU TWR. AFTER TKOF; WE SAW THAT A BEECHCRAFT BONANZA WAS TAKING OFF FROM RWY 35 WITHOUT CLRNC AND WAS ON A POTENTIAL COLLISION COURSE. WE CONTINUED TO CLB AND TURNED R TO A 360 DEG HDG TO AVOID A CONFLICT. AFTER THE BONANZA WAS NO LONGER A FACTOR; WE TURNED BACK TO RWY HDG. SUPPLEMENTAL INFO FROM ACN 418867: ON NOV/XA/98 APPROX XA30 LCL; I WAS AT HOU ARPT PREPARING FOR A CFI TRAINING FLT. I WAS HOLDING SHORT OF RWY 35 READY FOR TKOF. ANOTHER GRUMMAN CHEETAH WAS IN POS ON RWY 35 WAITING FOR RELEASE AND A B737 WAS TAXIING INTO POS ON RWY 30L. WHEN THE GRUMMAN CHEETAH IN FRONT OF ME WAS RELEASED; I WAS TOLD TO 'POS AND HOLD; RWY 35' BY HOU TWR. I TAXIED INTO POS AND WAITED FOR CLRNC TO TAKE OFF. WHILE TAXIING INTO POS; I NOTED AN AIRLINER ON ABOUT A 5 MI FINAL. NOTING THAT AIRPLANE; I WAS PRIMED FOR AN IMMEDIATE TKOF CLRNC. THE FOLLOWING IS WHAT I HEARD AND DID IN THE MINS THAT FOLLOWED: (TWR) -- '(GARBLE)...CLRED FOR IMMEDIATE TKOF RWY 35.' I ASSUMED THIS CLRNC WAS FOR ME AND WHILE STARTING MY TKOF ROLE ANSWERED: (ME) -- 'GRUMMAN N-NUMBER CLRED FOR IMMEDIATE TKOF RWY 35; WHAT HDG DO YOU WANT AFTER TKOF?' (TWR) -- 'FLY RWY HDG.' (ME) -- 'N-NUMBER; FLY RWY HDG.' I CONTINUED MY TKOF ROLL; LIFTED OFF STARTING MY CLB AND NOTICED THE B737 LIFTING OFF ON RWY 30L. IT BECAME CLR VERY QUICKLY WE WERE ON INTERSECTING PATHS AND I STARTED ALTERING COURSE TO THE W (L) AT THE SAME TIME THE B737 STARTED ALTERING COURSE TO THE N(R). I BELIEVE THAT THE 2 ACFT NEVER GOT CLOSER THAN 1500 FT HORIZ DISTANCE. SHORTLY AFTER TURNING; AN UNIDENTED VOICE; WHICH I BELIEVE WAS THE AIRLINE PLT ASKING HOU TWR IF 'THAT GRUMMAN' HAD BEEN CLRED FOR TKOF. THE QUESTION WAS ASKED 3 TIMES BEFORE HOU TWR ANSWERED NO. TWR THEN CONTACTED ME AND REPEATED THAT I HAD NOT BEEN CLRED FOR TKOF; THAT CLRNC WAS FOR THE B737. I APOLOGIZED FOR THE MISCOMS EXPLAINING THAT I THOUGHT THE CLRNC ISSUED WAS FOR ME AND ASKED WHAT THE TWR NEEDED ME TO DO. I WAS GIVEN A HDG OF 270 DEGS AND FLEW THAT HDG UNTIL CLR OF THE CLASS B AIRSPACE. THE REMAINDER OF THE FLT CONTINUED WITHOUT INCIDENT. THIS PROB AROSE BECAUSE OF THE FAST DELIVERY OF CLRNCS. HOU ARPT WAS VERY BUSY AT THAT TIME AND HOU TWR WAS DEALING WITH A LARGE NUMBER OF ACFT. CONTRIBUTING FACTORS INCLUDE THE SLIGHT GARBLE OF COMS IN THE BEGINNING; THE IMPROPER RWY GIVEN IN THE CLRNC TO THE B737; AND THE FAILURE OF ALL INVOLVED TO MAINTAIN CLR COMS. CLARIFICATION OF THE CLRNC SHOULD HAVE BEEN OBTAINED BY BOTH MYSELF AND THE AIRLINER; AND HOU TWR SHOULD HAVE CAUGHT THE MISTAKE WHEN I READ BACK A FAULTY CLRNC.