  The two dominant features in the distribution of orbital parameters for
close-in exoplanets are the prevalence of circular orbits for very short
periods, and the observation that planets on closer orbits tend to be heavier.
The first feature is interpreted as a signature of tidal evolution, while the
origin of the second, a "mass-period relation" for hot Jupiters, is not
understood. In this paper we re-consider the ensemble properties of transiting
exoplanets with well-measured parameters, focussing on orbital eccentricity and
the mass-period relation. We recalculate the constraints on eccentricity in a
homogeneous way, using new radial-velocity data, with particular attention to
statistical biases. We find that planets on circular orbits gather in a
well-defined region of the mass-period plane, close to the minimum period for
any given mass. Exceptions to this pattern reported in the Literature can be
attributed to statistical biases. The ensemble data is compatible with
classical tide theory with orbital circularisation caused by tides raised on
the planet, and suggest that tidal circularisation and the stopping mechanisms
for close-in planets are closely related to each other. The position
mass-period relation is compatible with a relation between a planet's Hill
radius and its present orbit.
