  We present results of magnetohydrodynamic (MHD) simulations of jet formation
and propagation, discussing a variety of astrophysical setups. In the first
approach we consider simulations of relativistic MHD jet formation, considering
jets launched from the surface of a Keplerian disk, demonstrating numerically -
for the first time - the self-collimating ability of relativistic MHD jets. We
obtain Lorentz factors up to about 10 while acquiring a high degree of
collimation of about 1 degree. We then present synchrotron maps calculated from
the intrinsic jet structure derived from the MHD jet formation simulation. We
finally present (non-relativistic) MHD simulations of jet lauching, treating
the transition between accretion and ejection. These setups include a physical
magnetic diffusivity which is essential for loading the accretion material onto
the outflow. We find relatively high mass fluxes in the outflow, of the order
of 20-40 % of the accretion rate.
