  The $r$-uniform expansion $F^{(r)+}$ of a graph $F$ is obtained by enlarging
each edge with $r-2$ new vertices such that altogether we use $(r-2)|E(F)|$ new
vertices. Two simple lower bounds on the largest number
$\mathrm{ex}_r(n,F^{(r)+})$ of $r$-edges in $F^{(r)+}$-free $r$-graphs are
$\Omega(n^{r-1})$ (in the case $F$ is not a star) and $\mathrm{ex}(n,K_r,F)$,
which is the largest number of $r$-cliques in $n$-vertex $F$-free graphs. We
prove that $\mathrm{ex}_r(n,F^{(r)+})=\mathrm{ex}(n,K_r,F)+O(n^{r-1})$. The
proof comes with a structure theorem that we use to determine
$\ex_r(n,F^{(r)+})$ exactly for some graphs $F$, every $r\chi(F)$ and
sufficiently large $n$.
