On uniformly resolvable {K_1,2, K_1,3}-designs

Given a collection of graphs H, a uniformly resolvable H-design of order v is a decomposition of the edges of K^v into isomorphic copies of graphs from H (also called blocks) in such a way that all blocks in a given parallel class are isomorphic to the same graph from H. We consider the case H={K_1,2, K_1,3} and prove that the necessary conditions on the existence of such designs are also sufficient.