Top: field lines of two twisted magnetosphere models in three dimensions. The dipolar field (model A) is shown on the left, and the combination of a dipolar and quadrupolar field (model B) is shown on the right. The same set of field lines is reproduced in intervals of π/2 in the azimuthal angle ϕ. In the current-free region (for P < P_c) there is no twist and the field lines are coplanar. Bottom: planar projection of some field lines in the top panels. The critical field line enclosing the toroidal region is highlighted with a thick line. The corresponding vacuum fields in both cases are shown as dotted lines in the background for comparison. The parameters and some calculated quantities for these two models are listed in Table 2.