DURING TAXI WITH WET SURFACE ACFT DEPARTED TXWY.

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AFTER UNEVENTFUL LNDG AT SAT; TURNED OFF RWY 3 AT THE END ONTO TXWY N WITH INSTRUCTIONS TO TAKE TXWY N TO TXWY D CROSS RWY 12L/R PROCEED TO THE RAMP. WX AT THE TIME WAS WET RAIN FALLING TEMP 41 DEGS DEWPOINT 39. THE TURN ONTO TXWY N NORMAL AND THE TRANSITION TO TXWY D WAS NORMAL. PRIOR TO RWY 12L; TXWY D MAKES A 45 DEG TURN TO THE L. I FELT AT ALL TIMES THAT TAXI SPD WAS CORRECT FOR THE CONDITIONS. UPON REACHING THE L TURN; I APPLIED L RUDDER WITH THE TAXI WHEEL WITH NO IMPACT. IMMEDIATE BRAKING WAS APPLIED TO NO AVAIL. THE ACFT SLID APPROX 45 FT TO THE EDGE OF THE TXWY WITH NO APPARENT LOSS OF FORWARD VELOCITY. IT HAPPENED SO QUICK AND UNEXPECTEDLY. WE STOPPED APPROX 30 FT IN THE DIRT. MAIN GEAR WERE STILL ON THE TXWY. NO DAMAGE TO ACFT OR GND EQUIP WERE NOTED. THE AREA AT THE TURN APPEARED QUITE SLICK ON INSPECTION. SUPPLEMENTAL INFO FROM ACN 331643: WE WERE ABOUT TO MAKE THE NEXT TURN TO THE L. THE CAPT MADE THE NOSEWHEEL STEERING INPUT AND I FELT THE PLANE MAKE A SLIGHT TURN TO THE L; THEN I FELT CHATTERING AND WE CONTINUED STRAIGHT; WHEN I WENT TO APPLY BRAKES; I NOTICED HE WAS ALREADY APPLYING THEM. I SAID REVERSERS! BUT IT WAS TOO LATE; WE HAD DEPARTED THE PAVEMENT. WE CAME TO A STOP A FEW SECONDS LATER WITH OUR NOSE ABOUT 30 FT OFF THE TXWY AND THE MAINS STILL ON THE TXWY. UPON OBSERVING THE TXWY I COULD SEE OUR SKID MARKS A GOOD DISTANCE 75-100 FT BEHIND US. ADDITIONALLY THE ARPT AUTHS STATED THIS TXWY HAS HAD NUMEROUS TXWY EXCURSIONS AT THE SAME SPOT AND ESPECIALLY AFTER HVY RAINS. LAST YR THE CITY EVEN ADDED A SEALANT TO ASSIST IN WATER DRAINAGE BUT THAT ONLY ADDED TO THE PROB SINCE IT MAKES THAT PORTION VERY SLIPPERY.