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We investigate spherical, isothermal and polytropic steady accretion modelsin the presence of the cosmological constant. Exact solutions are found forthree classes of isothermal fluids, assuming the test gas approximation. Thecosmological constant damps the mass accretion rate and - above certain limit -completely stops the steady accretion onto black holes. A "homoclinic-type"accretion flow of polytropic gas has been discovered in AdS spacetimes in thetest-gas limit. These results can have cosmological connotation, through theEinstein--Straus vacuole model of embedding local structures intoFriedman-Lemaitre-Robertson-Walker spacetimes. In particular one infers thatsteady accretion would not exist in the late phases of the Penrose's scenarioof the evolution of the Universe, known as the Weyl curvature hypothesis.

Spherical steady accretion flows -- dependence on the cosmological constant, exact isothermal solutions and applications to cosmology