We discuss the concept of Y-junctions for matter waves and investigate their guidance properties, focusing on the case of Bose-Einstein condensates with attractive interatomic interactions. We examine both discrete and continuous models, respectively relevant to Y-junctions formed in optical lattices (OL) and magnetic traps (MT). We find a strong dependence of the transmitted fraction of the condensate (in the OL case) on the angle with a maximum (per arm) of approximately 30%. In the MT case, we show that the presence of the junction's wedge can prevent collapse of the original condensate. (C) 2003 Elsevier B.V. All rights reserved.