The evolution of a stellar dipolar-type magnetosphere interacting with a Ke
plerian disk is investigated numerically using the ideal MHD ZEUS-3D code i
n the axisymmetry option. We compute the innermost region around the stella
r object using a non-smoothed gravitational potential. The disk is taken as
a boundary condition prescribing the mass inflow into the corona. Dependin
g mainly on the magnetic held strength, our simulations last several hundre
d Keplerian periods of the inner disk. The main result is that the dipolar
structure of the magnetic field almost completely disappears. An expanding
bubble of hot gas of low density forms disrupting the initial dipolar field
structure. A disk wind accelerates within the time limit of the simulation
to velocities of about 0.5 the Keplerian speed and potentially may develop
into a stationary collimated jet. We argue that non-stationary jet phenome
na should probably caused by a time-dependent disk. Simulations with a rota
ting and a non-rotating star show significant differences. In the case of a
rotating star during the very first time steps a high speed outflow along
the axis is initiated which does not exist in the case of a non-rotating st
ar.