  We present an analytical formula for the position and shape of the spots on
the surface of accreting magnetized stars in cases where a star has a dipole
magnetic field tilted at a small misalignment angle Theta < 30 degrees about
the rotational axis, and the magnetosphere is 2.5-5 times the radius of the
star. We observed that the azimuthal position of the spots varies significantly
when the position of the inner disc varies. In contrast, the polar position of
the spots varies only slightly because of the compression of the magnetosphere.
The azimuthal width of the spots strongly varies with Theta: spots have the
shape of an arc at larger misalignment angles, and resemble a ring at very
small misalignment angles. The polar width of the spots varies only slightly
with changes in parameters. The motion of the spots in the azimuthal direction
can provide phase-shifts in accreting millisecond pulsars, and the "drift" of
the period in Classical T Tauri stars. The position and shape of the spots are
determined by three parameters: misalignment angle Theta; normalized corotation
radius, r_c/R_* and normalized magnetospheric radius, r_m/R_*, where R_* is the
stellar radius.
  We also use our data to check the formula for the Alfv\'en radius, where the
main dependencies are r_m \sim (\mu^2/\dot M)^{2/7}, where \mu is the magnetic
moment of the star, and \dot M is the accretion rate. We found that the
dependence is more gradual, r_m \sim (\mu^2/\dot M)^{1/5}, which can be
explained by the compression of the magnetosphere by the disc matter and by the
non-dipole shape of the magnetic field lines of the external magnetosphere.
