Previously unexplored accretion regimes associated with the rotation of accreting matter, namely the perturbations of a quasi-spherical subsonic settling flow and Bondi-Hoyle accretion in the presence of axial rotation, are considered within the framework of ideal hydrodynamics. For subsonic settling accretion, the perturbations are shown to grow rapidly as the gravitating center is approached, so that the flow in the inner regions can no longer be considered as quasi-spherical. For Bondi-Hoyle accretion, a vacuum cylindrical cavity is shown to be formed at large distances from the gravitating center near the flow axis, with the flow velocity outside this cavity being virtually independent of the distance to the rotation axis.

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