Young stellar object jets are supersonic and highly collimated plasma outflows that propagate for large distances. Although their association to star formation is a well established fact, there are still open questions such as whether the outflow is of disk or stellar origin, how the jet’s time variable structure is produced and why there is an asymmetry between the opposite bipolar flows. The increasing angular resolution of modern telescopes gradually provides the clues to clarify and understand such issues. An emerging picture is that of a two-component protostellar jet, where a high mass loss rate disk wind surrounds a hot stellar outflow. In this context, our group has carried out numerical simulations of several two-component magnetohydrodynamic jet models, setting as initial conditions a combination of two well studied analytical solutions. We investigated the dynamics and the steady state features of many interesting cases as a function of the mixing parameters and the enforced time variability. A highly significant result was the morphological reproduction of the large scale knot-like structure of many young stellar objects jets. Moreover, with the assumption of a quadrupolar disk field we found asymmetric velocities between the bipolar outflows suggesting a possible explanation for this observational fact. In this article we summarize the results on the dynamics and the velocity profiles of a few interesting two-component jet scenarios.