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Let $X$ be a closed hyperbolic surface and $\lambda, \eta$ be weightedgeodesic multicurves which are short on X. We show that the iterated graftingalong $\lambda$ and $\eta$ is close in the Teichmueller metric to graftingalong a single multicurve which can be given explicitly in terms of $\lambda$and $\eta$.  Using this result, we study the holonomy lifts $gr_{\lambda}\rho_{X,\lambda}$of Teichmueller geodesics $\rho_{X,\lambda}$ for integral laminations $\lambda$and show that all of them have bounded Teichmueller distance to the geodesic$\rho_{X,\lambda}$. We obtain analogous results for grafting rays.  Finally we consider the asymptotic behaviour of iterated grafting sequences$\gr_{n\lambda}X$ and show that they converge geometrically to a puncturedsurface.

Iterated grafting and holonomy lifts of Teichmüller space