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In this paper, results are presented from studies of the dynamics of the plasma-current sheath and current distribution in the PF-3 facility, one of the largest plasma focus machines in the world. The experiments were done at input energy of W = 290 kJ and discharge current of I ~ 2 MA, with the chamber being stationary filled with the working gas. The current sheath parameters were measured with absolutely calibrated magnetic probes installed at different distances from the system axis and at different heights above the anode plane. The possibility is demonstrated of the formation of closed current loops due to the development of shunting breakdowns in the insulator region. The maximum residual plasma density at which the electrode gap remains magnetically self-insulated is estimated.