We consider the steady axisymmetric motion of an electrically conducting fluid contained within a spherical shell and permeated by a centred axial dipole magnetic field, which is strong as measured by the Hartmann number M. Slow motion is driven by rotating the inner boundary relative to the stationary outer boundary. For M >> 1, viscous effects are only important in Hartmann boundary layers adjacent to the inner and outer boundaries and a free shear-layer on the magnetic field line C tangent at Eo to the outer boundary at the equatorial plane of symmetry. We measure the ability to leak electric current into the solid boundaries by the size of their relative conductance epsilon. The nature of the flow is sensitive to the value of epsilon, because electric current leakage weakens the strength of the Hartmann layers. The work extends an earlier study of the case of a conducting inner boundary and an insulating outer boundary epsilono=0 (Dormy, E., Jault, D. & Soward, A.M. 2002, A super-rotating shear layer in magnetohydrodynamic spherical Couette flow. J.Fluid Mech. 452, 263-291) to other values of the outer boundary conductance epsilono. The main thrust of our development builds on the perfectly conducting boundary limit \epsilon_o\to\infty. Both analytic and numerical results are reported.