  Techniques of `dynamic renormalization', developed earlier for undirected
percolation and the contact model, are adapted to the setting of directed
percolation, thereby obtaining solutions of several problems for directed
percolation on $Z^d$ where $d \ge 2$. The first new result is a type of
uniqueness theorem: for every pair $x$ and $y$ of vertices which lie in
infinite open paths, there exists almost surely a third vertex $z$ which is
joined to infinity and which is attainable from $x$ and $y$ along directed open
paths. Secondly, it is proved that a random walk on an infinite directed
cluster is transient, almost surely, when $d \ge 3$. And finally, the block
arguments of the paper may be adapted to systems with infinite range, subject
to certain conditions on the edge probabilities.
