  We obtain the high energy, small angle, 2-particle gravitational scattering
amplitudes in topologically massive gravity (TMG) and its two non-dynamical
constituents, Einstein and Chern--Simons gravity. We use 't Hooft's approach,
formally equivalent to a leading order eikonal approximation: one of the
particles is taken to scatter through the classical spacetime generated by the
other, which is idealized to be lightlike. The required geometries are derived
in all three models; in particular, we thereby provide the first explicit
asymptotically flat solution generated by a localized source in TMG. In
contrast to $D$=4, the metrics are not uniquely specified, at least by naive
asymptotic requirements -- an indeterminacy mirrored in the scattering
amplitudes. The eikonal approach does provide a unique choice, however. We also
discuss the discontinuities that arise upon taking the limits, at the level of
the solutions, from TMG to its constituents, and compare with the analogous
topologically massive vector gauge field models.
