Context. At super-Eddington rates accretion flows onto black holes have been described as slim (aspect ratio H/R ≲ 1) or thick (H/R> 1) discs, also known as tori or (Polish) doughnuts. The relation between the two descriptions has never been established, but it was commonly believed that at sufficiently high accretion rates slim discs inflate, becoming thick.Aims. We wish to establish under what conditions slim accretion flows become thick.Methods. We use analytical equations, numerical 1 + 1 schemes, and numerical radiative MHD codes to describe and compare various accretion flow models at very high accretion rates. Results. We find that the dominant effect of advection at high accretion rates precludes slim discs becoming thick. Conclusions. At super-Eddington rates accretion flows around black holes can always be considered slim rather than thick.