  In this paper we are interested in the following question: Given an arbitrary
Steiner triple system $S$ on $m$ vertices and any 3-uniform hypertree $T$ on
$n$ vertices, is it necessary that $S$ contains $T$ as a subgraph provided $m
\geq (1+\mu)n$? We show the answer is positive for a class of hypertrees and
conjecture that the answer is always positive.
