We study the one-way flow model of network formation with owner-homogeneous link costs and heterogeneous profits. Recently, several proofs of existence of Nash networks are discussed in literature. The proof by Billand et al. (Econ Theory, 2007, forthcoming) is based on a nice and clear idea, but the technical elaboration is tedious and too complex in our opinion. In this note, we provide an alternative and easy accessible proof based on the same idea. Also, we show by means of a counterexample that Nash networks may not exist for games where link costs are heterogeneous, but arbitrarily close to owner-homogeneity.