Recent observations of jets in young stellar objects suggest that although both disk- and stellar-outflows seem to be present, each one of these two components may dominate at the various stages of the YSO. Over the past several years the only analytical solutions of the steady-state MHD equations which have been studied, correspond to the radially (magneto-centrifugally driven disk winds) and meridionally (thermally accelerated stellar outflows) self-similar models. In this context, we study through time dependent numerical simulations, using the PLUTO code, one prototypical case of each of these two classes examining many of their physical and numerical properties. We find that the solutions are structurally stable and robust, maintaining all their well defined features, despite several modifications they have been subject to. Therefore, their proper matching could explain a two-component jet.