  We show that any grafting ray in Teichm\"{u}ller space is (strongly)
asymptotic to some Teichm\"{u}ller geodesic ray. As an intermediate step we
introduce surfaces that arise as limits of these degenerating Riemann surfaces.
Given a grafting ray, the proof involves a Teichm\"{u}ller ray with a
conformally equivalent limit, and building quasiconformal maps of low
dilatation between the surfaces along the rays. Our preceding work had proved
the result for rays determined by an arational lamination or a multicurve, and
the unified approach here gives an alternative proof of the former case.
