  We study the $F$-decomposition threshold $\delta_F$ for a given graph $F$.
Here an $F$-decomposition of a graph $G$ is a collection of edge-disjoint
copies of $F$ in $G$ which together cover every edge of $G$. (Such an
$F$-decomposition can only exist if $G$ is $F$-divisible, i.e. if $e(F)\mid
e(G)$ and each vertex degree of $G$ can be expressed as a linear combination of
the vertex degrees of $F$.)
  The $F$-decomposition threshold $\delta_F$ is the smallest value ensuring
that an $F$-divisible graph $G$ on $n$ vertices with
$\delta(G)\ge(\delta_F+o(1))n$ has an $F$-decomposition. Our main results imply
the following for a given graph $F$, where $\delta_F^\ast$ is the fractional
version of $\delta_F$ and $\chi:=\chi(F)$:
  (i) $\delta_F\le \max\{\delta_F^\ast,1-1/(\chi+1)\}$;
  (ii) if $\chi\ge 5$, then
$\delta_F\in\{\delta_F^{\ast},1-1/\chi,1-1/(\chi+1)\}$;
  (iii) we determine $\delta_F$ if $F$ is bipartite.
  In particular, (i) implies that $\delta_{K_r}=\delta^\ast_{K_r}$. Our proof
involves further developments of the recent `iterative' absorbing approach.
