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The modclling of plasma outfiows from central gravitating objects such as AGN is bricfly discussed via analytic examples in the context of ideal MHD. The exact solutions are produced via a nonlinear separation of the variables in the full set of the MHD equations. Attention is given to the questions of initial acceleration and collimation of the outflow. A quantitative: criterion is provided for the transition of the morphologies from highly collimated jets to non collimated winds.

Astronomical observations, analytical solutions and numerical simulations have provided the building blocks to formulate the current theory of young stellar object jets. Although each approach has made great progress independently, it is only during the last decade that significant efforts are being made to bring the separate pieces together. Building on previous work that combined analytical solutions and numerical simulations, we apply a sophisticated cooling function to incorporate optically thin energy losses in the dynamics. On the one hand, this allows a self-consistent treatment of the jet evolution and on the other, it provides the necessary data to generate synthetic emission maps. Firstly, analytical disk and stellar outflow solutions are properly combined to initialize numerical two-component jet models inside the computational box. Secondly, magneto-hydrodynamical simulations are performed in 2.5D, following properly the ionization and recombination of a maximum of $29$ ions. Finally, the outputs are post-processed to produce artificial observational data. The first two-component jet simulations, based on analytical models, that include ionization and optically thin radiation losses demonstrate promising results for modeling specific young stellar object outflows. The generation of synthetic emission maps provides the link to observations, as well as the necessary feedback for the further improvement of the available models., accepted for publication A&A, 20 pages, 11 figures

The two types of Fanaroff-Riley radio loud galaxies, FRI and FRII, exhibit strong jets but with different properties. These differences may be associated to the central engine and/or the external medium. Aims: The AGN classification FRI and FRII can be linked to the rate of electromagnetic Poynting flux extraction from the inner corona of the central engine by the jet. The collimation results from the distribution of the total electromagnetic energy across the jet, as compared to the corresponding distribution of the thermal and gravitational energies. We use exact solutions of the fully relativistic magnetohydrodynamical (GRMHD) equations obtained by a nonlinear separation of the variables to study outflows from a Schwarzschild black hole corona. A strong correlation is found between the jet features and the energetic distribution of the plasma of the inner corona which may be related to the efficiency of the magnetic rotator. It is shown that observations of FRI and FRII jets may be partially constrained by our model for spine jets. The deceleration observed in FRI jets may be associated with a low magnetic efficiency of the central magnetic rotator and an important thermal confinement by the hot surrounding medium. Conversely, the strongly collimated and accelerated FRII outflows may be self collimated by their own magnetic field because of the high efficiency of the central magnetic rotator., Comment: Accepted for publication in the A&A