Meridional cuts of the rotation rate normalised to the value at the outer sphere (first and third panels) and toroidal field (second and fourth panels), in the quasi-steady state. In black lines are also represented the poloidal field lines (first and third panels) and the streamlines associated with the electrical-current function defined in Appendix A (second and fourth panels). The dotted (solid) lines then correspond to an anticlockwise (clockwise) current circulation. In the first two panels, the contraction does not advect the poloidal field lines and the quasi-steady state is achieved after ∼0.04τ_c (i.e. ∼ 20τ_Ap, see Fig. 2). In the last two panels such an advection is allowed and the quasi-steady configuration is reached after ∼1τ_c (i.e. after ∼100τ_Ap for this simulation). For these two cases, the Lundquist numbers are respectively L_u = 5 × 10⁴ and L_u = 10⁴ (runs D5 and D13). The other parameters are identical, namely P_r(N₀/Ω₀)² = 10⁴, E = 10⁻⁴, Re_c = 1, and P_m = 10².