In this paper, we consider some polytopes associated with arborescences in a series-parallel graph. Our main result is a complete characterization by linear inequalities of the convex hull of incidence vectors of rooted arborescences. As a consequence, we obtain a complete description of the Steiner arborescence polytype. We also suggest a new proof of Prodon et al.'s (1985) characterization of the dominant of the Steiner arborescence polytope. All our results are valid only if the underlying graph is series-parallel.
