  For smooth projective G-varieties, we equate the gauged Gromov-Witten
invariants for sufficiently small area and genus zero with the invariant part
of equivariant Gromov-Witten invariants. As an application we deduce a gauged
version of abelianization for Gromov-Witten invariants. In the symplectic
setting, we prove that any sequence of genus zero symplectic vortices with
vanishing area has a subsequence that converges after gauge transformation to a
holomorphic map with zero average moment map.
