  The selfgravity of an infalling gas can alter significantly the accretion of
gases. In the case of spherically symmetric steady flows of polytropic perfect
fluids the mass accretion rate achieves maximal value when the mass of the
fluid is 1/3 of the total mass. There are two weakly accreting regimes, one
over-abundant and the other poor in fluid content. The analysis within the
newtonian gravity suggests that selfgravitating fluids can be unstable, in
contrast to the accretion of test fluids.
