  We numerically solve the Teukolsky equation in the time domain to obtain the
gravitational-wave emission of a small mass inspiraling and plunging into the
equatorial plane of a Kerr black hole. We account for the dissipation of
orbital energy using the Teukolsky frequency-domain gravitational-wave fluxes
for circular, equatorial orbits, down to the light-ring. We consider Kerr spins
$-0.99 \leq q \leq 0.99$, and compute the inspiral-merger-ringdown (2,2),
(2,1), (3,3), (3,2), (4,4), and (5,5) modes. We study the large-spin regime,
and find a great simplicity in the merger waveforms, thanks to the extremely
circular character of the plunging orbits. We also quantitatively examine the
mixing of quasinormal modes during the ringdown, which induces complicated
amplitude and frequency modulations in the waveforms. Finally, we explain how
the study of small mass-ratio black-hole binaries helps extending
effective-one-body models for comparable-mass, spinning black-hole binaries to
any mass ratio and spin magnitude.
