An asymptotic multipartite K\"uhn-Osthus theorem

In this paper we prove an asymptotic multipartite version of a well-known theorem of K"uhn and Osthus by establishing, for any graph $H$ with chromatic number $r$, the asymptotic multipartite minimum degree threshold which ensures that a large $r$-partite graph $G$ admits a perfect $H$-tiling. We also give the 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 and Zhao.