  Accretion onto black holes in wind-fed binaries and in collapsars forms small
rotating discs with peculiar properties. Such ``mini-discs'' accrete on the
free-fall time without help of viscosity and nevertheless can have a high
radiative efficiency. The inviscid mini-disc model was previously constructed
for a non-rotating black hole. We extend the model to the case of a spinning
black hole, calculate the structure and radiative efficiency of the disc and
find their dependence on the black hole spin. If the angular momenta of the
disc and the black hole are anti-aligned, a hydrodynamic analog of Penrose
process takes place.
