  We present global 3D MHD simulations of geometrically thin but unstratified
accretion disks in which a near Keplerian disk rotates between two bounding
regions with initial rotation profiles that are stable to the MRI. The inner
region models the boundary layer between the disk and an assumed more slowly
rotating central, non magnetic star. We investigate the dynamical evolution of
this system in response to initial vertical and toroidal fields imposed in a
variety of domains contained within the near Keplerian disk. Cases with both
non zero and zero net magnetic flux are considered and sustained dynamo
activity found in runs for up to fifty orbital periods at the outer boundary of
the near Keplerian disk. Simulations starting from fields with small radial
scale and with zero net flux lead to the lowest levels of turbulence and
smoothest variation of disk mean state variables. For our computational set up,
average values of the Shakura & Sunyaev (1973) $\alpha$ parameter in the
Keplerian disk are typically $0.004\pm 0.002.$ Magnetic field eventually always
diffuses into the boundary layer resulting in the build up of toroidal field
inward angular momentum transport and the accretion of disk material. The mean
radial velocity, while exhibiting large temporal fluctuations is always
subsonic. Simulations starting with net toroidal flux may yield an average
$\alpha \sim 0.04.$ While being characterized by one order of magnitude larger
average $\alpha$, simulations starting from vertical fields with large radial
scale and net flux may lead to the formation of persistent non-homogeneous,
non-axisymmetric magnetically dominated regions of very low density.
