  Hypertrees are linear hypergraphs where every two vertices are connected by a
unique path. Elliott and R\"{o}dl conjectured that for any given $\mu>0$, there
exists $n_0$ such that the following holds. Every $n$-vertex Steiner triple
system contains all hypertrees with at most $(1-\mu)n$ vertices whenever $n\geq
n_0$. We prove this conjecture.
