Axisymmetric magnetohydrodynamic (MHD) simulations have been made of t
he formation of jets from a Keplerian disk threaded by a magnetic fiel
d. The disk is treated as a boundary condition, where matter with high
specific entropy is ejected with a Keplerian azimuthal speed and a po
loidal speed less than the slow magnetosonic velocity, and where bound
ary conditions on the magnetic fields correspond to a highly conductin
g disk. Initially, the space above the disk, the corona, is filled wit
h high specific entropy plasma in the thermal equilibrium in the gravi
tational field of the central object. The initial magnetic field is po
loidal and is represented by the superposition of the fields of monopo
les located below the plane of the disk. The rotation of the disk twis
ts the initial poloidal magnetic field lines, and this twist propagate
s into the corona pushing matter into jet-like outflow in a cylindrica
l region. After the first ''switch-on wave'', which originates during
the first rotation period of the inner radius of the disk, the matter
outflowing from the disk starts to flow and accelerate in the z-direct
ion owing to both the magnetic and pressure gradient forces. The how a
ccelerates through the slow magnetosonic and Alfven surfaces and at la
rger distances through the fast magnetosonic surface. The flow velocit
y of the jet is approximately parallel to the z-axis, with the collima
tion mainly a result of the pinching force of the toroidal magnetic fi
eld. The energy Bur of the flow increases with increasing magnetic fie
ld strength on the disk. Some of the cases studied have been run for l
ong times, 60 rotation periods of the inner radius of the disk, and sh
ow indications of approaching a stationary state.