  There is a sufficiently large $N\in h\mathbb{N}$ such that the following
holds. If $G$ is a tripartite graph with $N$ vertices in each vertex class such
that every vertex is adjacent to at least $2N/3+2h-1$ vertices in each of the
other classes, then $G$ can be tiled perfectly by copies of $K_{h,h,h}$. This
extends work by two of the authors [Electron. J. Combin, 16(1), 2009] and also
gives a sufficient condition for tiling by any fixed 3-colorable graph.
Furthermore, we show that $2N/3+2h-1$ in our result can not be replaced by
$2N/3+ h-2$ and that if $N$ is divisible by $6h$, then we can replace it with
the value $2N/3+h-1$ and this is tight.
