  Given k>=2, we construct a (2k-2)-parameter family of properly embedded
minimal surfaces in H^2 x R invariant by a vertical translation T, called
Saddle Towers, which have total intrinsic curvature 4 pi(1-k), genus zero and
2k vertical Scherk-type ends in the quotient by T. As limits of those Saddle
Towers, we obtain Jenkins-Serrin graphs over ideal polygonal domains (with
total intrinsic curvature 2 pi(1-k)); we also get properly embedded minimal
surfaces which are symmetric with respect to a horizontal slice and have total
intrinsic curvature 4 pi(1-k), genus zero and k vertical planar ends.
