  The axisymmetric 3-D MHD outflow of a cold plasma from a magnetized and
rotating astrophysical object is numerically simulated with the purpose of
investigating the outflow's magnetocentrifugal acceleration and eventual
collimation. Gravity and thermal pressure are neglected while a split-monopole
is used to describe the initial magnetic field configuration. It is found that
the stationary final state depends critically on a single parameter alpha
expressing the ratio of the corotating speed at the Alfven distance to the
initial flow speed along the initial monopole-like magnetic fieldlines. Several
angular velocity laws have been used for relativistic and nonrelativistic
outflows. The acceleration of the flow is most effective at the equatorial
plane and the terminal flow speed depends linearly on alpha. Significant flow
collimation is found in nonrelativistic efficient magnetic rotators
corresponding to relatively larger than 1 values of alpha while very weak
collimation occurs in inefficient magnetic rotators with values of alpha
smaller than about 1. Part of the flow around the rotation and magnetic axis is
cylindrically collimated while the remaining part obtains radial asymptotics.
The transverse radius of the jet is inversely proportional to alpha while the
density in the jet grows linearly with alpha. For alpha greater than about 5
the magnitude of the flow in the jet remains below the fast MHD wave speed
everywhere. In relativistic outflows, no collimation is found in the supersonic
region for parameters typical for radio pulsars. All above results verify the
main conclusions of general theoretical studies on the magnetic acceleration
and collimation of outflows from magnetic rotators and extend previous
numerical simulations to large stellar distances.
