  We study the canonical structure of three-dimensional topologically massive
gravity with a cosmological constant, using the full power of Dirac's method
for constrained Hamiltonian systems. It is found that the dimension of the
physical phase space is two per spacetime point, which corresponds to a single
Lagrangian degree of freedom. The analysis of the AdS asymptotic region reveals
a remarkable relation to 3D gravity with torsion: in the limit of vanishing
torsion, the conserved charges and asymptotic symmetries of the two theories
become identical.
