  A ``hyperideal circle pattern'' in $S^2$ is a finite family of oriented
circles, similar to the ``usual'' circle patterns but such that the closed
disks bounded by the circles do not cover the whole sphere. Hyperideal circle
patterns are directly related to hyperideal hyperbolic polyhedra, and also to
circle packings.
  To each hyperideal circle pattern, one can associate an incidence graph and a
set of intersection angles. We characterize the possible incidence graphs and
intersection angles of hyperideal circle patterns in the sphere, the torus, and
in higher genus surfaces. It is a consequence of a more general result,
describing the hyperideal circle patterns in the boundaries of geometrically
finite hyperbolic 3-manifolds (for the corresponding $\C P^1$-structures). This
more general statement is obtained as a consequence of a theorem of Otal
\cite{otal,bonahon-otal} on the pleating laminations of the convex cores of
geometrically finite hyperbolic manifolds.
