  In their paper, Bounds on the Number of Edges in Hypertrees, G.Y. Katona and
P.G.N. Szab\'o introduced a new, natural definition of hypertrees in
$k$-uniform hypergraphs and gave lower and upper bounds on the number of edges.
They also defined edge-minimal, edge-maximal and $l$-hypertrees and proved an
upper bound on the edge number of $l$-hypertrees.
  In the present paper, we verify the asymptotic sharpness of the
$\binom{n}{k-1}$ upper bound on the number of edges of $k$-uniform hypertrees
given in the above mentioned paper. We also make an improvement on the upper
bound of the edge number of $2$-hypertrees and give a general extension
construction with its consequences.
  We give lower and upper bounds on the maximal number of edges of $k$-uniform
edge-minimal hypertrees and a lower bound on the number of edges of $k$-uniform
edge-maximal hypertrees. In the former case, the sharp upper bound is
conjectured to be asymptotically $\frac{1}{k-1}\binom{n}{2}$.
