  For general off-shell N=2 supergravity-matter systems in three spacetime
dimensions, a formalism is developed to reduce the corresponding actions from
superspace to components. The component actions are explicitly computed in the
cases of Type I and Type II minimal supergravity formulations. We describe the
models for topologically massive supergravity which correspond to all the known
off-shell formulations for three-dimensional N=2 supergravity. We also present
a universal setting to construct supersymmetric backgrounds associated with
these off-shell supergravities.
