  We report on the fourth phase of our study of slightly rotating accretion
flows onto black holes. The main new element of this study is that we used
fully three dimensional (3-D) numerical simulations. We consider hydrodynamics
of inviscid accretion flows. We assume a spherically symmetric density
distribution at the outer boundary, but brake the flow symmetry by introducing
a small, latitude-dependent angular momentum. We also consider cases where
angular momentum at large radii is latitude- and azimuth-dependent. For the
latitude-dependent angular momentum, 3-D simulations confirm axisymmetric
results: the material that has too much angular momentum to be accreted forms a
thick torus near the equator. Consequently, accretion proceeds only through the
polar funnel, and the mass accretion rate through the funnel is constrained by
the size and shape of the torus, not by the outer conditions. In 3-D
simulations, we found that the torus precesses, even for axisymmetric
conditions at large radii. For the latitude and azimuth-dependent angular
momentum, the non-rotating gas near the equator can also significantly affect
the evolution of the rotating gas. In particular, it may prevent the formation
of a proper torus (i.e. its closing, in the azimuthal direction). In such
models, the mass accretion rate is only slightly less than the corresponding
Bondi rate.
