Axisymmetric magnetohydrodynamic (MHD) simulations are used to study t
he evolution of general magnetic field configurations where a magnetic
held B threads different radii of a differentially rotating accretion
disk. The differential rotation of the footpoints of B held loops at
different radii on the disk surface causes a twisting of the coronal m
agnetic field, an increase in the coronal magnetic energy, and an open
ing of the loops in the region where the magnetic pressure is larger t
han the matter pressure (beta less than or similar to 1). In the regio
n where beta greater than or similar to 1, the loops may be only parti
ally opened. Current layers form in the narrow regions that separate o
ppositely directed magnetic field lines. Reconnection occurs in these
layers as a result of the small numerical magnetic diffusivity of the
code. In contrast with the case of the solar coronal magnetic held, th
e combination of magnetic and centrifugal forces leads to significant
matter outflow from the disk. The faster rotation of the inner part of
the disk gives a stronger outflow from this part of the disk. The out
flow accelerates with increasing distance from the disk up to velociti
es in excess of the escape speed. The outflows show some collimation w
ithin the computational region and have a large power output mainly in
the form of a Poynting flux. Thus these outflows are pertinent to the
origin of astrophysical jets. We present results of a survey of simul
ation runs for the behavior of magnetic loops and outflows for a wide
range of held strengths B and mass outflow sates (M) over dot(j). The
model and processes observed are relevant to the coronae of accretion
disks around stellar-mass objects, including pre-main-sequence stars,
compact stars, and black holes, as well as the coronae of disks around
massive black holes in active galactic nuclei. Opening of magnetic he
ld loops may lead to transient and/or steady outflows, while reconnect
ion events may be responsible for X-ray flares in such objects.