  We give finiteness results and some classifications up to diffeomorphism of
minimal strong symplectic fillings of Seifert fibered spaces over S^2
satisfying certain conditions, with a fixed natural contact structure. In some
cases we can prove that all symplectic fillings are obtained by rational
blow-downs of a plumbing of spheres. In other cases, we produce new manifolds
with convex symplectic boundary, thus yielding new cut-and-paste operations on
symplectic manifolds containing certain configurations of symplectic spheres.
