  Given a bipartite graph $H$ and an integer $n$, let $f(n;H)$ be the smallest
integer such that, any set of edge disjoint copies of $H$ on $n$ vertices, can
be extended to an $H$-design on at most $n+f(n;H)$ vertices. We establish tight
bounds for the growth of $f(n;H)$ as $n \rightarrow \infty$. In particular, we
prove the conjecture of F\"uredi and Lehel \cite{FuLe} that $f(n;H) = o(n)$.
This settles a long-standing open problem.
