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We present the first results of a global axisymmetric simulation of accretion onto rotating magnetized stars from a turbulent, MRI-driven disk. The angular momentum is transported outward by the magnetic stress of the turbulent flow with a rate corresponding to a Shakura-Sunyaev viscosity parameter alpha\approx 0.01-0.04. The result of the disk-magnetosphere interaction depends on the orientation of the poloidal field in the disk relative to that of the star at the disk-magnetosphere boundary. If fields have the same polarity, then the magnetic flux is accumulated at the boundary and blocks the accretion which leads to the accumulation of matter at the boundary. Subsequently, this matter accretes to the star in outburst before accumulating again. Hence, the cycling, `bursty' accretion is observed. If the disc and stellar fields have opposite polarity, then the field reconnection enhances the penetration of the disk matter towards the deeper field lines of the magnetosphere. However, the magnetic stress at the boundary is lower due to the field reconnection. This decreases the accretion rate and leads to smoother accretion at a lower rate. Test simulations show that in the case of higher accretion rate corresponding to alpha=0.05-0.1, accretion is bursty in cases of both polarities. On the other hand, at much lower accretion rates corresponding to alpha < 0.01, accretion is not bursty in any of these cases. We conclude that the episodic, bursty accretion is expected during periods of higher accretion rates in the disc, and in some cases it may alternate between bursty and smooth accretion, if the disk brings the poloidal field of alternating polarity. We find that a rotating, magnetically-dominated corona forms above and below the disk, and that it slowly expands outward, driven by the magnetic force.