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 a 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 the 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