  We study several problems of clearing subgraphs by mobile agents in digraphs.
The agents can move only along directed walks of a digraph and, depending on
the variant, their initial positions may be pre-specified. In general, for a
given subset~$\mathcal{S}$ of vertices of a digraph $D$ and a positive integer
$k$, the objective is to determine whether there is a subgraph
$H=(\mathcal{V}_H,\mathcal{A}_H)$ of $D$ such that (a) $\mathcal{S} \subseteq
\mathcal{V}_H$, (b) $H$ is the union of $k$ directed walks in $D$, and (c) the
underlying graph of $H$ includes a Steiner tree for $\mathcal{S}$ in $D$. We
provide several results on the polynomial time tractability, hardness, and
parameterized complexity of the problem.
