  We present optimal online algorithms for two related known problems involving
Steiner Arborescence, improving both the lower and the upper bounds. One of
them is the well studied continuous problem of the {\em Rectilinear Steiner
Arborescence} ($RSA$). We improve the lower bound and the upper bound on the
competitive ratio for $RSA$ from $O(\log N)$ and $\Omega(\sqrt{\log N})$ to
$\Theta(\frac{\log N}{\log \log N})$, where $N$ is the number of Steiner
points. This separates the competitive ratios of $RSA$ and the Symetric-$RSA$,
two problems for which the bounds of Berman and Coulston is STOC 1997 were
identical. The second problem is one of the Multimedia Content Distribution
problems presented by Papadimitriou et al. in several papers and Charikar et
al. SODA 1998. It can be viewed as the discrete counterparts (or a network
counterpart) of $RSA$. For this second problem we present tight bounds also in
terms of the network size, in addition to presenting tight bounds in terms of
the number of Steiner points (the latter are similar to those we derived for
$RSA$).
