Flow topology in the fiducial run (ambipolar diffusion only Λ_A = 1). Top row: poloidal streamlines (white) and log of the sonic Mach number. Bottom row: poloidal field and log of density, normalised so that the mid-plane density at R = 1 is unity. The colour scales are identical in the columns. From left to right, the disc magnetisation increases: β = 10⁵, 10³, and 35. The green lines denotes critical lines of the flow: Alfvénic (plain) and fast magnetosonic (dot-dashed). The dashed green line represents the disc “surface” where the flow becomes ideal, which is arbitrarily located at z = 3.5h for all of the solutions.