AT APPROXIMATELY 35MPH THE POWER STEERING OF MY 2003 MINI COOPER ERRATICALLY ENGAGED AND DISENGAGED SEVERAL TIMES. I RESPONDED BY SLOWING DOWN AND TRYING TO MAINTAIN CONTROL OF THE VEHICLE. ONCE STOPPED, I TURNED THE CAR OFF COMPLETELY. ONCE OUT OF THE VEHICLE I HEARD AN ELECTRIC MOTOR RUNNING. I OPENED THE HOOD TO INVESTIGATE AND NOTED A SMALL AMOUNT OF SMOKE RISING FROM THE AFT PORTION OF THE ENGINE COMPARTMENT. I WENT BACK TO THE IGNITION SWITCH TO CONFIRM IT WAS OFF AND REMOVED THE KEYS. THE ELECTRIC MOTOR CONTINUED TO RUN AND AS I WENT BACK TO THE OPEN HOOD THE SMOKE VOLUME HAD INCREASED DRAMATICALLY. THE SMOKE HAD A VERY CLEAR ELECTRICAL SMELL AND COLOR. I IMMEDIATELY BEGAN TRYING TO DISCONNECT THE BATTERY. WHILE OBTAINING TOOLS FROM THE HATCH OF THE CAR, THE ELECTRIC POWER STEERING PUMP ASSEMBLY ERUPTED IN FLAMES. I OBTAINED MY FIRE EXTINGUISHER AND DIRECTED IT AT THE AFT PORTION OF THE ENGINE COMPARTMENT. THIS PRODUCED NO RESULTS AND THE FLAMES RETURNED QUICKLY. I THEN GOT THE TOOLS FROM THE HATCH OF THE CAR AND CUT THE BATTERY CABLES. THIS CAUSED THE FIRE TO SUBSIDE IMMEDIATELY. AT THE REPAIR FACILITY THE POWER STEERING PUMP ASSEMBLY (ELECTRIC) WAS REMOVED AND DETERMINED TO BE THE CAUSE OF THE FIRE. THE FACT THAT I HAD TOOLS AND 25 YEARS MECHANICAL EXPERIENCE PREVENTED THIS CAR FROM BURNING TO THE GROUND. IN MY OPINION THIS IS A MAJOR SAFETY ISSUE ON TWO LEVELS. FIRST: LOSS OF DIRECTIONAL CONTROL. SECOND: FIRE HAZARD, ELECTRICAL COMPONENT THAT CANNOT BE TURNED OFF WI