The axisymmetric 3D MI-ID outflow of cold plasma from a magnetized and rota
ting astrophysical object is numerically simulated with the purpose of inve
stigating the magnetocentrifugal acceleration and eventual collimation of t
he outflow. Gravity and thermal pressure are neglected while a split monopo
le is used to describe the initial magnetic field configuration. It is foun
d that the stationary final state depends critically on a single parameter
a expressing the ratio of the corotating speed at the Alfven distance to th
e initial flow speed along the initial monopole-like magnetic field lines.
Several angular velocity laws have been used for relativistic and non-relat
ivistic outflows. The acceleration of the flow is most effective at the equ
atorial plane and the terminal flow speed depends Linearly on alpha. Signif
icant flow collimation is found in non-relativistic efficient magnetic rota
tors corresponding to relatively large values of alpha greater than or simi
lar to 1 while very weak collimation occurs in inefficient magnetic rotator
s with smaller values of alpha < 1. Part of the flow around the rotation an
d magnetic axis is cylindrically collimated while the remaining part obtain
s radial asymptotics. The transverse radius of the jet is inversely proport
ional to alpha while the density in the jet grows Linearly with alpha. For
alpha greater than or similar to 5 the magnitude of the flow in the jet rem
ains below the fast MHD wave speed everywhere. In relativistic outflows, no
collimation is found in the supersonic region for parameters typical for r
adio pulsars. All the above results verify the main conclusions of general
theoretical studies on the magnetic acceleration and collimation of outflow
s from magnetic rotators and extend previous numerical simulations to large
stellar distances.