  Kalai conjectured that every $n$-vertex $r$-uniform hypergraph with more than
$\frac{t-1}{r} {n \choose r-1}$ edges contains all tight $r$-trees of some
fixed size $t$. We prove Kalai's conjecture for $r$-partite $r$-uniform
hypergraphs. Our result is asymptotically best possible up to replacing the
term $\frac{t-1}{r}$ with the term $\frac{t-r+1}{r}$.
  We apply our main result in graphs to show an upper bound for the Tur\'an
number of trees.
