Using ab-initio methods we investigate the possibility of three-terminalgraphene "T-junction" devices and show that these all-graphene edge contactsare energetically feasible when the 1D interface itself is free from foreignatoms. We examine the energetics of various junction structures as a functionof the atomic scale geometry. Three-terminal equilibrium Green's functions areused to determine the transmission spectrum and contact resistance of thesystem. We find that the most symmetric structures have a significant bindingenergy, and we determine the contact resistances in the junction to be in therange of 1-10 kΩμm which is comparable to the best contact resistance reportedfor edge-contacted graphene-metal contacts. We conclude that conductingall-carbon T-junctions should be feasible.