  In this paper we study a family of generalizations of the Pontryagin and
Husain-Kucha\v{r} actions on manifolds with boundary. In some cases, they
describe well-known models---either at the boundary or in the bulk---such as
3-dimensional Euclidean general relativity with a cosmological constant or the
Husain-Kucha\v{r} model. We will use Hamiltonian methods in order to
disentangle the physical and dynamical content of the systems that we discuss
here. This will be done by relying on a geometric implementation of the Dirac
algorithm in the presence of boundaries recently proposed by the authors.
