  At super-Eddington rates accretion flows onto black holes have been described
as slim (aspect ratio $H/R \lesssim 1$) 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. We wish to establish under
what conditions slim accretion flows become thick. 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.We find that
the dominant effect of advection at high accretion rates precludes slim discs
becoming thick. At super-Eddington rates accretion flows around black holes can
always be considered slim rather than thick.
