  Asymptotic AdS Riemann space-times in five dimensions with a black brane
(horizon) sourced by a fully back-reacted scalar field (dilaton) offer -- via
the holographic dictionary -- various options for the thermodynamics of the
flat four-dimensional boundary theory, uncovering Hawking-Page, first-order and
second-order phase transitions up to a cross-over or featureless behavior. The
relation of these phase structures to the dilaton potential is clarified and
illustrating examples are presented. Having in mind applications to QCD we
study probe vector mesons with the goal to figure out conditions for forming
Regge type series of radial excitations and address the issue of meson melting.
