Observations have shown that in addition to a y component associated with the flaring of the tail, a net y component of the magnetic field can persist in the geomagnetic tail, roughly proportional to the interplanetary By. We use the tail equilibrium theory outlined by Birn (1987) to construct self-consistent three-dimensional models of the tail that include this effect. We find that the net ByN field varies only weakly along field lines and across the tail. The presence of the net ByN in the neutral sheet implies that a part of the cross-tail current becomes field-aligned, flowing from the southern to the northern hemisphere for ByN>0 and from north to south for ByN0 this opening occurs preferably on the north/dawn and south/dusk sides, producing an asymmetry and an apparent tilt of the closed field line plasma sheet region around the tail axis relative to the neutral sheet. We find also a topological connection of the low latitude region near the magnetopause with the plasma sheet boundary layer, separating closed plasma sheet and open lobe field lines. For ByN>0 this interconnection takes place on the north/dusk and south/dawn sides of the low latitude boundary region. ¿ American Geophysical Union 1990