  We describe the results of numerical "2.5--dimensional" MHD simulations of an
initially unmagnetized disk model orbiting a central point--mass and responding
to the continual generation of poloidal magnetic field due to a secular source
that emulates the Poynting--Robertson (PR) drag on electrons in the vicinity of
a luminous stellar or compact accreting object. The fluid in the disk and in
the surrounding hotter atmosphere has finite electrical conductivity and allows
for the magnetic field to diffuse freely out of the areas where it is
generated, while at the same time, the differential rotation of the disk twists
the poloidal field and quickly induces a substantial toroidal--field component.
The secular PR term has dual purpose in these simulations as the source of the
magnetic field and the trigger of a magnetorotational instability (MRI) in the
disk. The MRI is especially mild and does not destroy the disk because a small
amount of resistivity dampens the instability efficiently. In simulations with
moderate resistivities (diffusion timescales up to $\sim$16 local dynamical
times) and after $\sim$100 orbits, the MRI has managed to transfer outward
substantial amounts of angular momentum and the inner edge of the disk, along
with azimuthal magnetic flux, has flowed toward the central point--mass where a
new, magnetized, nuclear disk has formed. The toroidal field in this nuclear
disk is amplified by differential rotation and it cannot be contained; when it
approaches equipartition, it unwinds vertically and produces episodic jet--like
outflows. The poloidal field in the inner region cannot diffuse back out if the
characteristic diffusion time is of the order of or larger than the dynamical
time; it continues to grow linearly in time undisturbed and without saturation,
as the outer sections of many poloidal loops are being drawn radially outward.
