the black-hole (naked-singularity) backgrounds as they become asymptotically de Sitter and contain a cosmological event horizon behind which the spacetime is dynamic. Properties of the circular geodesic orbits in the Schwarzschild–de Sitter (SdS) and Reissner–Nordström–de Sitter (RNdS) spacetimes show that due to the presence of the RRCC, the thin discs have not only an inner edge determined (approximately) by the radius of the innermost stable circular orbit, but also an outer edge given by the radius of the outermost stable circular orbit, located nearby the static radius.[@Stu-Hle:1999:PHYSR4:; @Stu-Hle:2002:ACTPS2:] The vicinity of the static radius can be considered as a counterpart to the asymptotically flat region of the Kerr spacetimes, as can be demonstrated by the embedding diagrams of the equatorial plane of both the directly projected geometry and the optical reference geometry reflecting some hidden properties of the geodesic motion.[@Abr-Pra:1990:MONNR:; @Stu-Hle:2000:CLAQG:; @Hle:2002:JB60:] The analysis of equilibrium configurations of perfect fluid orbiting in the SdS black-hole backgrounds shows a possible existence of thick discs with outflow of matter through an outer cusp of the equilibrium configuration due to violation of mechanical equilibrium.[@Stu-Sla-Hle:2000:ASTRA:] Such an outflow can represent a strong stabilizing effect[@Rez-Zan-Fon:2003:ASTRA:] against the runaway instability[@Abr-Cal-Nob:1983:NATURE:] of thick discs orbiting the SdS 