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This paper deals with simulation of cathode-spot motion in the self-consistent magnetic field in 3-D formulation. Plasma jets are modeled as cylinders of a small radius, their conductivity depending on the magnetic field. Electrodes are modeled in their actual 3-D geometry. The magnitude and direction of the velocity of the cathode-spot motion versus the magnetic-field components are taken from the experimental data on the motion of a single spot. The dependence of the cathode-jet conductivity on the magnetic field is found by means of interpolating the Volt-Tesla characteristics (VTCs) for a single spot from the same work. Use is made of the mechanism for spot splitting at currents exceeding some threshold of the current and spot destruction at currents lower than another threshold. Attainment of the steady state by the voltage across the discharge was studied and found to take place after the spots reach the electrode edge. The temporal dependences of the histograms of spot distribution in the current were derived. The obtained results are used to plot the VTC of a system of spots. The qualitative behavior of the dependences agrees with experiment, which is an argument in favor of the assumption that the behavior of a high-current arc is determined to a large extent by that of a system of individual cathode spots interacting via the common self-consistent magnetic field.