  We discuss a fine-tuning of rather generic three dimensional higher-curvature
gravity actions that leads to gauge symmetry enhancement at the linearized
level via partial masslessness. Requiring this gauge symmetry to be present
also non-linearly reduces such actions to conformal Chern-Simons gravity. We
perform a canonical analysis of this theory and construct the gauge generators
and associated charges. We provide and classify admissible boundary conditions.
The boundary conditions on the conformal equivalence class of the metric render
one chirality of the partially massless Weyl gravitons normalizable and the
remaining one non-normalizable. There are three choices - trivial, fixed or
free - for the Weyl factors of the bulk metric and of the boundary metric. This
proliferation of boundary conditions leads to various physically distinct
scenarios of holography that we study in detail, extending considerably the
discussion initiated in 1106.6299. In particular, the dual CFT may contain an
additional scalar field with or without background charge, depending on the
choices above.
