Left: illustration of the topology of equipotential surfaces that determines the spatial distribution of fluid in thick discs (often called Polish doughnuts). The yellow region corresponds to tori of various thicknesses. The orange (along with yellow) region corresponds to a torus with a cusp. The topology allows for many discs with no cusp (β <  β_cusp) and one disc with a cusp (β = β_cusp). The self-crossing equipotential curve corresponds to the marginally overflowing torus with ℓ_K(r_ms) < ℓ_c <  ℓ_K(r_mb). The torus has a finite extent and is terminated by a cusp located at its inner edge. The coloured lines corresponding to constant radii denote the marginally stable (ISCO) and marginally bound (r_mb) orbit. A more detailed illustration along with rigorous classification of possible equipotential curve topologies can be found in Abramowicz et al. (1978). Right: equipressure contours seen within an up-to-date general relativistic three-dimensional global radiative magnetohydrodynamic simulation. The figure is based on the work of Lančová et al. (2019) who reported a new class of realistic solutions of BH accretion flows – the so-called puffy accretion discs. The setup of the simulation is very general and does not assume any form of initial toroidal structure of the fluid within the inner accretion region.