  We discuss the global properties of static, spherically symmetric
configurations of a self-gravitating real scalar field $\phi$ in general
relativity (GR), scalar-tensor theories (STT) and high-order gravity ($L=f(R)$)
in various dimensions. In GR, for fields with arbitrary potentials $V(\phi)$,
not necessarily positive-definite, it is shown that the list of all possible
types of space-time causal structure in the models under consideration is the
same as the one for $\phi = const$. In particular, there are no regular black
holes with any asymptotics. These features are extended to STT and $f(R)$
theories, connected with GR by conformal mappings, unless there is a conformal
continuation, i.e., a case when a singularity in a solution of GR maps to a
regular surface in an alternative theory, and the solution is continued through
such a surface. This effect is exemplified by exact solutions in GR with a
massless conformal scalar field, considered as a special STT. Necessary
conditions for the existence of a conformal continuation are found; they only
hold for special choices of STT and high-order theories of gravity.

General Relativity and Quantum Cosmology