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