  We build equilibrium solutions of magnetised thick discs around a highly
spinning Kerr black hole and evolve these initial data up to a final time of
about 100 orbital periods. The numerical simulations reported in this paper
solve the general relativistic magnetohydrodynamics equations using the BHAC
code and are performed in axisymmetry. Our study assumes non-self-gravitating,
polytropic, constant angular momentum discs endowed with a purely toroidal
magnetic field. In order to build the initial data we consider three
approaches, two of which incorporate the magnetic field in a self-consistent
way and a third approach in which the magnetic field is included as a
perturbation on to an otherwise purely hydrodynamical solution. To test the
dependence of the evolution on the initial data, we explore four representative
values of the magnetisation parameter spanning from almost hydrodynamical discs
to very strongly magnetised tori. The initial data are perturbed to allow for
mass and angular momentum accretion on to the black hole. Notable differences
are found in the long-term evolutions of the initial data. In particular, our
study reveals that highly magnetised discs are unstable, and hence prone to be
fully accreted and expelled, unless the magnetic field is incorporated into the
initial data in a self-consistent way.
