Magnetohydrodynamic simulations have been made of the formation of out
flows from a Keplerian disk threaded by a magnetic held. The disk is t
reated as a boundary condition, where matter is ejected with Keplerian
azimuthal speed and poloidal speed less than the slow magnetosonic ve
locity, and where boundary conditions on the magnetic field correspond
to a highly conducting disk. Initially, the space above the disk, the
corona, is filled with high specific entropy plasma in thermal equili
brium in the gravitational potential of the central object. The initia
l magnetic field is poloidal and is represented by a superposition of
monopoles located below the plane of the disk. The rotation of the dis
k twists the initial poloidal magnetic field, and this twist propagate
s into the corona pushing and collimating matter into jetlike outflow
in a cylindrical region. Matter outflowing from the disk flows and acc
elerates in the z-direction owing to both the magnetic and pressure gr
adient forces. The flow accelerates through the slow magnetosonic and
Alfven surfaces and at larger distances through the fast magnetosonic
surface. The flow velocity of the jet is approximately parallel to the
z-axis, and the collimation results from the pinching force of the to
roidal magnetic field. For a nonrotating disk no collimation is observ
ed.