  Disc-winds originating from the inner parts of accretion discs are considered
as the basic component of magnetically collimated outflows. The only available
analytical MHD solutions to describe disc-driven jets are those characterized
by the symmetry of radial self-similarity. However, radially self-similar MHD
jet models, in general, have three geometrical shortcomings, (i) a singularity
at the jet axis, (ii) the necessary assumption of axisymmetry, and (iii) the
non-existence of an intrinsic radial scale, i.e. the jets formally extend to
radial infinity. Hence, numerical simulations are necessary to extend the
analytical solutions towards the axis, by solving the full three-dimensional
equations of MHD and impose a termination radius at finite radial distance. We
focus here on studying the effects of relaxing the (ii) assumption of
axisymmetry, i.e. of performing full 3D numerical simulations of a disc-wind
crossing all magnetohydrodynamic critical surfaces. We compare the results of
these runs with previous axisymmetric 2.5D simulations. The structure of the
flow in all simulations shows strong similarities. The 3D runs reach a steady
state and stay close to axisymmetry for most of the physical quantities, except
for the poloidal magnetic field and the toroidal velocity which slightly
deviate from axisymmetry. The latter quantities show signs of instabilities,
which, however, are confined to the region inside the fast magnetosonic
separatrix surface. The forces present in the flow, both of collimating and
accelerating nature, are in good agreement in both the 2.5D and the 3D runs. We
conclude that the analytical solution behaves well also after relaxing the
basic assumption of axisymmetry.
