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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

Three‐dimensional Magnetohydrodynamic Simulations of an Accretion Disk with Star‐Disk Boundary Layer