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The high-current vacuum arcs (HCVA) with high average current densities (J0 les 3 kA/cm2) in strong axial magnetic fields (AMFs) Bn les 1.2 T were studied. The typical V-shape of Volt-Tesla characteristic (VTC) has been shown to retain in strong AMF and at raising the current density, the quantitative parameters change, though. The nature and causes of the changes are discussed. The main factors to define VTC in strong AMF have been shown to be the electrode material and the arc length. It has been confirmed the conclusion of our previous work that, in strong AMF, the cathode attachment size for an arc in a quasi-stationary state is defined by AMF induction and arc length. The quantitative comparison of VTC and voltage of a low-current arc under the action of magnetic field, inclined to the arc axis, encounters difficulties arising in describing of HCVA as an aggregate of independent cathode jets at moderate values of the AMF induction.