  (Abridged) Finite radius accretion disks are a strong candidate for launching
astrophysical jets from their inner parts and disk-winds are considered as the
basic component of such magnetically collimated outflows. The only available
analytical MHD solutions for describing disk-driven jets are those
characterized by the symmetry of radial self-similarity. Radially self-similar
MHD models, in general, have two geometrical shortcomings, a singularity at the
jet axis and 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 and impose a physical
boundary at finite radial distance. We focus here on studying the effects of
imposing an outer radius of the underlying accreting disk (and thus also of the
outflow) on the topology, structure and variability of a radially self-similar
analytical MHD solution. The initial condition consists of a hybrid of an
unchanged and a scaled-down analytical solution, one for the jet and the other
for its environment. In all studied cases, we find at the end steady
two-component solutions.
