BE40 CREW FOUND A VERY BUSY CTLR THAT WAS APCHING OVERLOAD. THE CTLR SEPARATED TFC IN AN ACCEPTABLE AND LEGAL MANNER.

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I WAS CLRED BY LZU TWR TO FAM VIA RADAR VECTORS; CHOO-CHOO CLB TO 5000 FT; EXPECT FL350 AFTER 5 MINS; DEP FREQ OF 119.3 AND XPONDER CODE OF XYZA. I READ BACK CLRNC AND REQUESTED IDENT OF CHOO-CHOO WHICH TWR GAVE AS GQO AND ACKNOWLEDGED READBACK CORRECT. WE WAITED FOR 5-6 GA FIXED WING; RECIPROCATING DEPS AND WERE CLRED FOR TKOF; WITH A TURN TO APPROX 310 DEGS WHEN WE HAD VISUAL OF LIGHT RECIPROCATING; WHICH TOOK OFF PREVIOUSLY TO ENTER TFC PATTERN. AFTER TKOF; WE INDICATED WE HAD LIGHT ACFT IN SIGHT AND TURNED TO APPROX 310 DEGS. DURING TURN; WE WERE CLRED TO ZTL; DEP FREQ; RPTED IN AND CONTINUED CLB TO 5000 FT. I HEARD MANY XMISSIONS FROM CTR TO OTHER ACFT AS HE WAS SATURATED. WE HAD A SILENT COCKPIT; AND WERE MONITORING AND I WAS HAND FLYING. WE HEARD ONE CALL ENDING IN 'D;' WHICH WAS NOT ABCD. I THEN HEARD CALL FOR ANOTHER ACFT (ACR HVY) TO MAKE A R DSNDING TURN AS IT WAS DSNDING THROUGH 8000 FT. I HEARD ANOTHER CALL WHICH INSTRUCTED ME TO 'TURN L NOW.' I THOUGHT TO 180 DEGS. I STARTED TURN TO L; AS COPLT ATTEMPTED TO VERIFY HDG. CTR TOLD US TO TURN TO 270 DEGS. I STEADIED AT 270 DEGS (ALL THIS TIME I HAD LARGE ACFT IN R DSNDING TURN AT MY 2 O'CLOCK POS; 2000-3000 FT ABOVE; 8-10 NM AWAY). THEN CTR INSTRUCTED ME TO MAKE A R CLBING TURN TO 310 DEGS AND 8000 FT. FMS TCASII NEVER INDICATED LESS THAN 1900 FT DIFFERENTIAL WHILE IT WAS ILLUMINATED; WHICH WAS DURING INITIAL TURN TO SOUTHERLY; STOPPING ON 270 DEGS. DURING MY TURN BACK N; WHILE CONTINUING TO CLB TO 8000 FT; THE TFC PASSED FROM 2 O'CLOCK HIGH; LEVEL AT 11:30 - 9:45 O'CLOCK POS LOW. IT NEVER APPEARED TO GET CLOSER THAN 2 MI. ATC CTLR APPEARED TOTALLY SATURATED. I DID NOT CONSIDER THIS AN NMAC AND DO NOT FEEL IT WOULD HAVE BECOME ONE; YET DON'T KNOW WHAT THE CTLR PLANNED TO DO WITH OTHER JET. CTLR CHANGED US OVER TO ANOTHER CTLR; WHICH I THINK WAS ZTL; FOLLOWED SHORTLY BY ZME. I WAS VFR; FLYING ON AN IFR CLRNC.