  Given a fixed $k$-uniform hypergraph $F$, the $F$-removal lemma states that
every hypergraph with few copies of $F$ can be made $F$-free by the removal of
few edges. Unfortunately, for general $F$, the constants involved are given by
incredibly fast-growing Ackermann-type functions. It is thus natural to ask for
which $F$ one can prove removal lemmas with polynomial bounds. One trivial case
where such bounds can be obtained is when $F$ is $k$-partite. Alon proved that
when $k=2$ (i.e. when dealing with graphs), only bipartite graphs have a
polynomial removal lemma. Kohayakawa, Nagle and R\"odl conjectured in 2002 that
Alon's result can be extended to all $k>2$, namely, that the only $k$-graphs
$F$ for which the hypergraph removal lemma has polynomial bounds are the
trivial cases when $F$ is $k$-partite. In this paper we prove this conjecture.
