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 and also its evolutionary stage. In this context, we study a numerical model based on such a two-component outflow by using as an initial condition a combination of two prototypical models, each describing a meridionally self-similar and a radially self-similar exact solution of the steady-state, ideal hydromagnetic equations. These two classes of radially and meridionally self-similar solutions, have already been well studied and have been found to be related to the properties of disk- and stellar-wind, respectively. By properly mixing the two solutions, a variety of models is constructed with different contribution weights for each component in the initial set-up. The models are evolved in time by using the PLUTO code and the interaction and co-existence of the two components in the jet is investigated. It is found that a steady-state is always reached, independently of the mixing parameters of the two model ingredients. Moreover, the final outcome of the time evolution stays rather close to the initial analytical solutions. The results are compared and discussed along the lines of recent observational data.