  We present results of 3D simulations of MHD instabilities at the accretion
disk-magnetosphere boundary. The instability is Rayleigh-Taylor, and develops
for a fairly broad range of accretion rates and stellar rotation rates and
magnetic fields. It manifests itself in the form of tall, thin tongues of
plasma that penetrate the magnetosphere in the equatorial plane. The shape and
number of the tongues changes with time on the inner-disk dynamical timescale.
In contrast with funnel flows, which deposit matter mainly in the polar region,
the tongues deposit matter much closer to the stellar equator. The instability
appears for relatively small misalignment angles, $\Theta\lesssim30^\circ$,
between the star's rotation and magnetic axes, and is associated with higher
accretion rates. The hot spots and light curves during accretion through
instability are generally much more chaotic than during stable accretion. The
unstable state of accretion has possible implications for quasi-periodic
oscillations and intermittent pulsations from accreting systems, as well as
planet migration.
