The paper deals with the operation of Hall plasma thrusters and the transversal to the magnetic field current in such systems. The problems of the transverse conductivity and related processes are treated in the framework of the well-known Morozov's model; the difference is in the addition of the mechanism of plasma recombination on the walls of the thruster and further volume ionization of the neutrals created at the walls. The distribution functions of the neutrals and secondary electrons generated by ionization are found, as well as the expression for the transverse current. The obtained result contains an additional correcting factor compared to the conventional Morozov's equation for this current and permits a better quantitative agreement of the theoretical expression and experimental results.