Elliott–Rödl's hypertree embedding conjecture for Steiner triple systems

A hypertree is a $3$-uniform hypergraph in which every two vertices are connected by a unique path. A Steiner triple system is a $3$-uniform hypergraph in which every pair of vertices belongs to exactly one hyperedge. Elliott–Rödl's conjecture. Given $\mu\geq 0$, there exists $n_0=n_0(\mu)$ such that if $n\geq n_0$, $T$ is any hypertree on $n$ vertices, and $S$ is any Steiner triple system on $m\geq n(1+\mu)$ vertices, then $T$ is a subhypergraph of $S$. The paper presents this as an asymptotic step toward determining the largest order of a hypertree guaranteed in every Steiner triple system, and its proof establishes the stated result.