  We study a solvable class of five-dimensional dilaton gravity models that
continuously interpolate between anti-de Sitter (AdS$_5$), linear dilaton
(LD$_5$) and positively curved spacetimes as a function of a continuous
parameter $\nu$. The dilaton vacuum expectation value is set by a potential
localized on a flat brane. We chart the elementary properties of these
backgrounds for any admissible $\nu$, and determine stability conditions of the
brane-dilaton system. We find that the spectrum of metric fluctuations can be
either continuous or discrete. It features a massless graviton mode confined
between the brane and the curvature singularity, and a massive radion mode tied
to brane-dilaton stability. We show that, in the presence of a bulk black hole,
the holographic theory living on the brane features a perfect fluid. The
equation of state of the holographic fluid interpolates between radiation,
pressureless matter and vacuum energy as a function of $\nu$. This extends
earlier findings on holographic fluids. Our results suggest that the
thermodynamics of the fluid mirrors precisely the thermodynamics of the bulk
black hole.
