  We show results of global 3D MHD simulations of accretion onto stars with
superposition of the dipole and octupole fields, where we vary the ratio
between components. Simulations show that if octupolar field strongly dominates
at the disc-magnetosphere boundary, then matter flows into the ring-like
octupolar poles, forming ring-shape spots at the surface of the star above and
below equator. The light-curves are complex and may have two peaks per period.
In case where the dipole field dominates, matter accretes in two ordered funnel
streams towards poles, however the polar spots are meridionally-elongated due
to the action of the octupolar component. In the case when the fields are of
similar strengths, both, polar and belt-like spots are present. In many cases
the light-curves show the evidence of complex fields, excluding the cases of
small inclinations angles, where sinusoidal light-curve %is observed and
`hides' the information about the field complexity. We also propose new
mechanisms of phase shift in stars with complex magnetic fields. We suggest
that the phase shifts can be connected with: (1) temporal variation of the
star's intrinsic magnetic field and subsequent redistribution of main magnetic
poles; (2) variation of the accretion rate, which causes the disc to interact
with the magnetic fields associated with different magnetic moments. We use our
model to demonstrate these phase shift mechanisms, and we discuss possible
applications of these mechanisms to accreting millisecond pulsars and young
stars.
