relict repulsive cosmological constant (RRCC), $\Lambda > 0$, or some kind of similarly acting quintessence, has to be invoked in order to explain the dynamics of the recent Universe.[@Bah-etal:1999:SCIEN:; @Kol-Tur:1990:EarUni:]

There is a strong “concordance” indication[@Spe-etal:2003:ASTJS:] that the observed value of the vacuum energy density is $$\varrho_{\mathrm{vac(0)}}\approx 0.73 \varrho_{\rm crit(0)}$$ with present values of the critical energy density $\varrho_{\rm crit(0)}$, and the Hubble parameter $H_{0}$ given by $$\varrho_{\rm crit(0)}=\frac{3H_{0}^2}{8\pi},\quad H_{0}=100h\
      \rm{km}\ \rm{s}^{-1}\ \rm{Mpc}^{-1}.$$ Taking value of the dimensionless parameter $h\approx 0.7$, we obtain the RRCC to be $$\Lambda_{0}=8\pi\varrho_{\mathrm{vac(0)}}\approx 1.3 \times 10^{-56}\
      \rm{cm}^{-2}. 
\label{E3}$$

It is well known that the RRCC strongly influences expansion of the Universe, leading finally to an exponentially accelerated stage.[@Car-Ost:1996:ModAst:] However, surprisingly enough, the RRCC can be relevant for accretion processes in the field of central black holes in quasars and active galactic nuclei.

Basic properties of geometrically thin accretion discs with low accretion rates and negligible pressure are given by the circular geodetical motion in the black-hole backgrounds,[@Nov-Tho:1973:BlaHol:436] while for geometrically thick discs with high accretion rates and relevant pressure they are determined by equipotential surfaces of test perfect fluid rotating in the backgrounds.[@Koz-Jar-Abr:1978:ASTRA:; @Abr-Jar-Sik:1978:ASTRA:] The presence of the RRCC changes substantially the asymptotic structure of 