Azimuthal velocity of thin disks from our simulations with Ω = 0.2 Ω_ms. As expected from theory, it closely follows the Keplerian curve and is uniform on cylinders (with corrections of order z²/r²). The disk-corona interface is at z ≈ 2. This and later figures exhibit values in the initial set-up (thin black solid line), and the quasi-stationary solutions in the numerical simulations in the HD (dot-dashed black line), and the MHD (long-dashed line) cases. Black, green, blue, and red colors correspond to stellar magnetic field strength (0.35, 0.7, 1.05, 1.4) , respectively (cf. the final paragraph of Appendix B). The closest match (in normalization) of the analytic profile to the case is depicted with triangle symbols. Left panel: radial dependence along the midplane, just above θ = 90°. Insert shows a zoom into the vicinity of the stellar surface, where the inner boundary condition affects the solution so that it is different than in the purely HD case. Right panel: the profiles along a vertical line at r = 15R_⋆. The thin black solid line, sloping down at z ≈ 2 in the right panel, indicates v_φ in the initial set-up. The legend describes the line styles also for the following three figures.