  We resolve two problems of [Cameron, Praeger, and Wormald -- Infinite highly
arc transitive digraphs and universal covering digraphs, Combinatorica 1993].
First, we construct a locally finite highly arc-transitive digraph with
universal reachability relation. Second, we provide constructions of 2-ended
highly arc transitive digraphs where each `building block' is a finite
bipartite graph that is not a disjoint union of complete bipartite graphs. This
was conjectured impossible in the above paper. We also describe the structure
of 2-ended highly arc transitive digraphs in more generality, although complete
characterization remains elusive.
