The formation of thin current sheets is a common feature of the late substorm growth phase in the magnetotail of the Earth. The location and the structure of the evolving thin current sheet determine the onset and the dynamic phase of magnetic substorms. To determine the formation and further evolution of thin current sheets in the near-Earth magnetotail, we employ a two-fluid model of electrons and ions, the Hall-MHD. We start from a two-dimensional tail-equilibrium model and apply a plasma inflow from the lobes to simulate the presubstorm loading process of the tail. Our results confirm recent 2.5-dimensional particle and hybrid simulations which have shown thin current sheet formation, with the majority of the new current supported by the electrons. The Hall-MHD simulations are extended to a current sheet thinning model with three-dimensional driving conditions and different magnetic field boundary conditions. We investigated the changes to the tail magnetic and current structure brought about by the cross-tail magnetic field components generated by Hall electric fields. For all these cases, the additional current is carried by the electrons, with very small effects of magnetic field and driving boundary conditions. ¿ 1999 American Geophysical Union