  Broadcasting in a computer network is a method of transferring a message to
all recipients simultaneously. It is common in this situation to use a tree
with many leaves to perform the broadcast, as internal nodes have to forward
the messages received, while leaves are only receptors. We consider the
subjacent problem of, given a directed graph~$D$, finding a spanning
arborescence of D, if one exists, with the maximum number of leaves. In this
paper, we concentrate on the class of rooted directed acyclic graphs, for which
the problem is known to be MaxSNP-hard. A 2-approximation was previously known
for this problem on this class of directed graphs. We improve on this result,
presenting a (3/2)-approximation. We also adapt a result for the undirected
case and derive an inapproximability result for the vertex-weighted version of
Maximum Leaf Spanning Arborescence on rooted directed acyclic graphs.
