  We study the general-relativistic dynamics of matter being accreted onto and
ejected by a magnetised and nonrotating neutron star. The dynamics is followed
in the framework of fully general relativistic magnetohydrodynamics (GRMHD)
within the ideal-MHD limit and in two spatial dimensions. More specifically,
making use of the numerical code BHAC, we follow the evolution of a
geometrically thick matter torus driven into accretion by the development of a
magnetorotational instability. By making use of a number of simulations in
which we vary the strength of the stellar dipolar magnetic field, we can
determine self-consistently the location of the magnetospheric (or Alfv\'en)
radius $r_{\rm msph}$ and study how it depends on the magnetic moment $\mu$ and
on the accretion rate. Overall, we recover the analytic Newtonian scaling
relation, i.e. $r_{\rm msph} \propto B^{4/7}$, but also find that the
dependence on the accretion rate is very weak. Furthermore, we find that the
material torque correlates linearly with the mass-accretion rate, although both
of them exhibit rapid fluctuations. Interestingly, the total torque fluctuates
drastically in strong magnetic field simulations and these unsteady torques
observed in the simulations could be associated with the spin fluctuations
observed in X-ray pulsars.
