  We numerically investigate limits of a two-parameter family of stationary
solutions to the Einstein-Vlasov system. The solutions are toroidal and have
non-vanishing angular momentum. As one tunes to more relativistic solutions
(measured for example by an increasing redshift) there exists a sequence of
solutions which approaches the extreme Kerr black hole family. Solutions with
angular momentum larger than the square of the mass are also investigated, and
in the relativistic limit the near-field geometry of such solutions is observed
to become conical in the sense that there is a deficit angle. Such solutions
may provide self-consistent models for rotating circular cosmic strings.
