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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 weintroduce surfaces that arise as limits of these degenerating Riemann surfaces.Given a grafting ray, the proof involves a Teichm\"{u}ller ray with aconformally equivalent limit, and building quasiconformal maps of lowdilatation between the surfaces along the rays. Our preceding work had provedthe result for rays determined by an arational lamination or a multicurve, andthe unified approach here gives an alternative proof of the former case.

Conformal limits of grafting and Teichm\"{u}ller rays and their asymptoticity