  We report on the first global three-dimensional (3D) MHD simulations of disk
accretion onto a rotating magnetized star through the Rayleigh-Taylor
instability. The star has a dipole field misaligned relative to the rotation
axis by a small angle Theta. Simulations show that, depending on the accretion
rate, a star may be in the stable or unstable regime of accretion. In the
unstable regime, matter penetrates deep into the magnetosphere through several
elongated "tongues" which deposit matter at random places on the surface of the
star, leading to stochastic light-curves. In the stable regime, matter accretes
in ordered funnel streams and the light-curves are almost periodic. A star may
switch between these two regimes depending on the accretion rate and may thus
show alternate episodes of ordered pulsations and stochastic light-curves. In
the intermediate regime, both stochastic and ordered pulsations are observed.
For Theta > 30 degrees, the instability is suppressed and stable accretion
through funnel streams dominates.
