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In this paper we prove an asymptotic multipartite version of a well-knowntheorem of K\"uhn and Osthus by establishing, for any graph $H$ with chromaticnumber $r$, the asymptotic multipartite minimum degree threshold which ensuresthat a large $r$-partite graph $G$ admits a perfect $H$-tiling. We also givethe threshold for an $H$-tiling covering all but a linear number of vertices of$G$, in a multipartite analogue of results of Koml\'os and of Shokoufandeh andZhao.

An asymptotic multipartite K\"uhn-Osthus theorem