Turbulence is the most promising mechanism to explain the anomalous enhancement of angular momentum transport (AMT) in astrophysical accretion discs that power some of the most energetic phenomena in the universe. The presence of even weak magnetic fields can destabilize an otherwise (Rayleigh-) stable Keplerian disc leading to the development of the magneto-rotational instability (MRI) and to MRI driven turbulence. Inspired by the Princeton MRI liquid gallium experiment, we present numerical simulations of circular and magnetized Couette flow in axisymmetric and fully three-dimensional geometry of the cylindrical annulus. The incompressible Navier-Stokes and magneto-hydrodynamical equations are solved with the spectral element code Nek5000 incorporating realistic boundary conditions corresponding to differentially rotating rings. Our results** demonstrate a significant enhancement of AMT and its dependence on Reynolds number, horizontal boundary conditions and external magnetic field strength through the onset of unsteadiness and three-dimensionality. Finally, at high enough magnetic Reynolds number, the MRI driven turbulence becomes an efficient dynamo capable of sustaining the magnetic fields necessary to induce MRI in the first place. This implies that MRI-driven turbulence in a real disc is likely to be self-regulating and universal depending only on the properties of the disc itself.