  We study the maximum number $ex(n,e,H)$ of copies of a graph $H$ in graphs
with given number of vertices and edges. We show that for any fixed graph $H$,
$ex(n,e,H)$ is asymptotically realized by the quasi-clique provided that the
edge density is sufficiently large. We also investigate a variant of this
problem, when the host graph is bipartite.
