A COMMERCIAL PILOT ON A POSITIONING FLIGHT EXPERIENCED A FUEL EXHAUSTION TOTAL POWER LOSS FOLLOWING AN ABRUPT CLIMB MANEUVER, AND LANDED ON THE TUNDRA. ENGINE AND FUEL SYSTEM BY FAA INSPECTORS EXAMINATION FOUND NO ANOMALIES. ONLY RESIDUAL FUEL WAS FOUND ON BOARD. WHEN LEVELED, THE ENGINE STARTED AND RAN NORMALLY. FUEL SPILLED UNDER VENT WAS AN 18 INCH PUDDLE IN SATURATED TUNDRA. THE PART 135 OPERATOR KEPT NO FUEL RECORDS, OR FLIGHT FOLLOWING RECORDS FOR THE FLIGHT.