This paper extends to all interplanetary magnetic field (IMF) orientations the qualitative convection pattern presented by Burch et al. (this issue), containing viscous, merging, and lobe cells driven, respectively, by diffusion or other quasi-viscous processes, merging of interplanetary fields with closed dayside field lines, and merging of interplanetary fields with open tail lobe field lines. The model is based on the antiparallel merging hypothesis of Crooker (1979a) with the addition of small but finite cells driven by quasi-viscous processes on the dawn and dusk edges of the polar cap. The data and model presented by Burch et al. pertained to southward IMF conditions. This paper generalizes that model and proposes a qualitative dependence of the three types of convection cells on the x, y, and z components of the IMF. For example, the lobe cell should be enhanced in the northern hemisphere if Bx < 0 and in the southern for Bx > 0, and, for a given Bx and Bz, should be larger as |By| increases. For northward IMF, the merging cell disappears, leaving only the lobe cell in a smaller polar cap. If the y component of the IMF (By) is small, we infer the four-cell pattern of Burke et al. (1979), with two counter-rotating lobe cells having sunward flow in the central polar cap and tailward flow on the flanks. If By is large, the antiparallel merging model predicts a single lobe cell filling the polar cap, whose direction of rotation depends on the sign of By and is opposite in opposite hemispheres. We argue that this vortex is unstable to reconnection in the magnetotail, leading to two (or more) vortices in each polar cap, each with the same sense of rotation, but again differing between the hemispheres. Each vortex has a region of closed field lines in the sunward-flowing section and open field lines in the antisunward-flowing section. This model encompasses several features of the theta arc phenomenon, and makes several predictions with respect to symmetries and antisymmetries between the two polar caps.