  Observations of collimated outflows in young stellar objects indicate that
several features of the jets can be understood by adopting the picture of a
two-component outflow, wherein a central stellar component around the jet axis
is surrounded by an extended disk-wind. The precise contribution of each
component may depend on the intrinsic physical properties of the YSO-disk
system as well as its evolutionary stage. In this context, the present article
starts a systematic investigation of two-component jet models via
time-dependent simulations of two prototypical and complementary analytical
solutions, each closely related to the properties of stellar-outflows and
disk-winds. These models describe a meridionally and a radially self-similar
exact solution of the steady-state, ideal hydromagnetic equations,
respectively. By using the PLUTO code to carry out the simulations, the study
focuses on the topological stability of each of the two analytical solutions,
which are successfully extended to all space by removing their singularities.
In addition, their behavior and robustness over several physical and numerical
modifications is extensively examined. It is found that radially self-similar
solutions (disk-winds) always reach a final steady-state while maintaining all
their well-defined properties. The different ways to replace the singular part
of the solution around the symmetry axis, being a first approximation towards a
two-component outflow, lead to the appearance of a shock at the super-fast
domain corresponding to the fast magnetosonic separatrix surface. Conversely,
the asymptotic configuration and the stability of meridionally self-similar
models (stellar-winds) is related to the heating processes at the base of the
wind.
