  Most giant exoplanets discovered by radial velocity surveys have much higher
eccentricities than those in the solar system. The planet--planet scattering
mechanism has been shown to match the broad eccentricity distribution, but the
highest-eccentricity planets are often attributed to Kozai-Lidov oscillations
induced by a stellar companion. Here we investigate whether the highly
eccentric exoplanet population can be produced entirely by scattering. We ran
500 N-body simulations of closely packed giant-planet systems that became
unstable under their own mutual perturbations. We find that the surviving bound
planets can have eccentricities up to $e > 0.99$, with a maximum of 0.999017 in
our simulations. This suggests that there is no maximum eccentricity that can
be produced by planet--planet scattering. Importantly, we find that extreme
eccentricities are not extremely rare; the eccentricity distribution for all
giant exoplanets with $e > 0.3$ is consistent with all planets concerned being
generated by scattering. Our results show that the discovery of planets with
extremely high eccentricities does not necessarily signal the action of the
Kozai-Lidov mechanism.
