We performed global three-dimensional magnetohydrodynamic simulations of accretion on to a star with magnetic field and other properties close to those observed in the classical T Tauri star BP Tau. We observed in the simulations that the disc is disrupted by the dipole component and matter flows towards the star in two funnel streams which form two accretion spots below the dipole magnetic poles. The octupolar component becomes dynamically important very close to the star and it redirects the matter flow to higher latitudes. The spots are meridionally elongated and are located at higher latitudes, compared with the pure dipole case. A series of simulation runs were performed at different accretion rates. We found that a 1.2 kG dipole field truncates the disc at a distance comparable to the corotation radius if the accretion rate is (1.4–2) × 10−9 M⊙ yr−1, which is at the lower end of the observationally derived values. If the accretion rate is somewhat higher, 8.5 × 10−9 M⊙ yr−1, then the disc is truncated at r≈ 3.6R★, which is a less favourable situation for the slowly rotating BP Tau. The magnetic torque acting on the star is also small; however, it is probably sufficient to support rotational equilibrium at the present state of slow rotation. Disc–magnetosphere interaction leads to inflation of the field lines and to the formation of magnetic towers above and below the disc. The magnetic field of BP Tau is close to potential inside the magnetospheric surface, where magnetic stress dominates over the matter stress. However, it strongly deviates from potential at larger distances from the star.