Conditions on the lowermost cells of the reference simulation K2. Here all parameters are traced along the first cell above the lower boundary : R = 1 and θ ∈ [0; π/2] on the source and then θ = π/2 and R ∈ [0; R_ext] on the disk. Shown are the Bernouilli invariant E, the toroidal and vertical magnetic field B_Φ and B_z, the mass to magnetic flux ratio η, the rotation speed of magnetic surfaces Ω_*, the speed of sound C_s and the vertical Alfvénic speed V_Az, over the magnetic flux Ψ. The black vertical line corresponds to the flux anchored at (R = 1,θ = π/2), at the source/disk interface.