  We present an $O(\log k)$-approximation for both the edge-weighted and
node-weighted versions of \DST in planar graphs where $k$ is the number of
terminals. We extend our approach to \MDST (in general graphs \MDST and \DST
are easily seen to be equivalent but in planar graphs this is not the case
necessarily) in which we get an $O(R+\log k)$-approximation for planar graphs
for where $R$ is the number of roots.
