  We study the orbital parameters distribution of stars that are scattered into
nearly radial orbits and then spiral into a massive black hole (MBH) due to
dissipation, in particular by emission of gravitational waves (GW). This is
important for GW detection, e.g. by the Laser Interferometer Space Antenna
(LISA). Signal identification requires knowledge of the waveforms, which depend
on the orbital parameters. We use analytical and Monte Carlo methods to analyze
the interplay between GW dissipation and scattering in the presence of a mass
sink during the transition from the initial scattering-dominated phase to the
final dissipation-dominated phase of the inspiral. Our main results are (1)
Stars typically enter the GW-emitting phase with high eccentricities. (2) The
GW event rate per galaxy is a few per Gyr for typical central stellar cusps,
almost independently of the relaxation time or the MBH mass. (3) For
intermediate mass black holes (IBHs) of ~a thousand solar masses such as may
exist in dense stellar clusters, the orbits are very eccentric and the inspiral
is rapid, so the sources are very short-lived.
