  The aim of this paper is to report on the existence of a wide variety of
exact solutions, ranging from black holes to wormholes, when a conformally
coupled scalar field with a self interacting potential containing a linear, a
cubic and a quartic self interaction is taken as a source of the
energy-momentum tensor, in the Einstein theory with a cosmological constant.
Among all the solutions there are two particularly interesting. On the one
hand, the spherically symmetric black holes when the cosmological constant is
positive; they are shown to be everywhere regular, namely there is no
singularity neither inside nor outside the event horizon. On the other hand,
there are spherically symmetric and topological wormholes that connect two
asymptotically (anti) de Sitter regions with a different value for the
cosmological constant. The regular black holes and the wormholes are supported
by everywhere regular scalar field configurations.
