In this paper we investigate a steady accretion within the Einstein-Straus vacuole, in the presence of the cosmological constant. The dark energy damps the mass accretion rate and --- above certain limit --- completely stops the steady accretion onto black holes, which in particular is prohibited in the inflation era and after (roughly) $10^{12}$ years from Big Bang (assuming the presently known value of the cosmological constant). Steady accretion would not exist in the late phases of the Penrose's scenario - known as the Weyl curvature hypothesis - of the evolution of the Universe.

misprints corrected, matches published version