  We report on the numerical discovery of quasi-periodic oscillations (QPOs)
associated with accretion through a non-axisymmetric magnetic boundary layer in
the unstable regime, when two ordered equatorial streams form and rotate
synchronously at approximately the angular velocity of the inner disk The
streams hit the star's surface producing hot spots. Rotation of the spots leads
to high-frequency QPOs. We performed a number of simulation runs for different
magnetospheric sizes from small to tiny, and observed a definite correlation
between the inner disk radius and the QPO frequency: the frequency is higher
when the magnetosphere is smaller. In the stable regime a small magnetosphere
forms and accretion through the usual funnel streams is observed, and the
frequency of the star is expected to dominate the lightcurve. We performed
exploratory investigations of the case in which the magnetosphere becomes
negligibly small and the disk interacts with the star through an equatorial
belt. We also performed investigation of somewhat larger magnetospheres where
one or two ordered tongues may dominate over other chaotic tongues. In
application to millisecond pulsars we obtain QPO frequencies in the range of
350 Hz to 990 Hz for one spot. The frequency associated with rotation of one
spot may dominate if spots are not identical or antipodal. If the spots are
similar and antipodal then the frequencies are twice as high. We show that
variation of the accretion rate leads to drift of the QPO peak.
