  Most of ultraluminous X-ray sources are thought to be objects accreting above
their Eddington limits. In the recently identified class of ultraluminous X-ray
pulsars, accretor is a neutron star and thus has a fairly small mass with a
small Eddington limit. The accretion disc structure around such an object
affects important observables such as equilibrium period, period derivative and
the size of the magnetosphere. We propose a model of a nearly-standard
accretion disc interacting with the magnetosphere only in a thin layer near the
inner disc rim. Our calculations show that the size of the magnetosphere may be
represented as the classical Alfv\'en radius times a dimensionless factor $\xi$
which depends on the disc thickness only. In the case of
radiation-pressure-dominated disc, the size of the magnetosphere does not
depend on the mass accretion rate. In general, increasing the disc thickness
leads to a larger magnetosphere size in units of the Alfv\'en radius. For large
enough mass accretion rates and magnetic moments, it is important to take into
account not only the pressure of the magnetic field and the radiation pressure
inside the disc, but also the pressure of the radiation produced close to the
surface of the neutron star in accretion column. The magnetospheric size may
increase by up to factor of two as a result of the effects related to the disc
thickness and the irradiation from the central source. Accounting for these
effects reduces the estimate of the neutron star magnetic moment by a factor of
several.
