Recent observations of jets in young stellar objects suggest that both disk- and stellar-winds are present, with the dominant component being dictated by the intrinsic physical conditions of the YSO system. In this context, we construct and evolve in time, using the PLUTO code, several numerical models by properly setting as an initial condition different contributions of a magneto-centrifugal driven disk wind and a thermally accelerated stellar jet. Such outflows are obtained from a radially and a meridionally self-similar exact solutions of the steady-state MHD equations, respectively. We find that all models reach a steady-state, in a few cases asymptotically. The final outcome of the simulations is found close enough to the initial configurations, thus retaining the validity of the analytical studies. Moreover, the magneto-centrifugally driven disk wind remains almost unmodified, while it effectively collimates the inner thermally driven stellar outflow. Proper choice of the parameters can explain the different cases of the two-component jets observed, i.e. from the one extreme of stellar dominated ones, up to the other, with the disk-wind being the only contributor.