  We perform axisymmetric relativistic magnetohydrodynamic (MHD) simulations to
investigate the acceleration and collimation of jets and outflows from disks
around compact objects. The fiducial disk surface (respectively a slow disk
wind) is prescribed as boundary condition for the outflow. We apply this
technique for the first time in the context of relativistic jets. The strength
of this approach is that it allows us to run a parameter study in order to
investigate how the accretion disk conditions govern the outflow formation. Our
simulations using the PLUTO code run for 500 inner disk rotations and on a
physical grid size of 100x200 inner disk radii. In general, we obtain
collimated beams of mildly relativistic speed and mass-weighted half-opening
angles of 3-7 degrees. When we increase the outflow Poynting flux by injecting
an additional disk toroidal field into the inlet, Lorentz factors up to 6 are
reached. These flows gain super-magnetosonic speed and remain Poynting flux
dominated. The light surface of the outflow magnetosphere tends to align
vertically - implying three relativistically distinct regimes in the flow - an
inner sub-relativistic domain close to the jet axis, a (rather narrow)
relativistic jet and a surrounding subrelativistic outflow launched from the
outer disk surface - similar to the spine-sheath structure currently discussed
for asymptotic jet propagation and stability. The outer subrelativistic disk
wind is a promising candidate for the X-ray absorption winds that are observed
in many radio-quiet AGN.
