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 few times 10-9 yr-1 for typical central stellar cusps, almost independently of the
relaxation time or the MBH mass.
(3) For intermediate mass black holes (IBHs) of ~103 Msun 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.