The transport properties of three Luttinger liquid wires (with possibly different interaction strength), connected through a Y-junction, are studied within the scattering state formalism. The case of a symmetric set-up without magnetic flux is considered first, for which the scattering matrix and the matrix of conductances is parametrized by two variables. For these we derive coupled RG equations, with one-loop contributions summed to infinite order of bulk interaction. The Y-junction pierced by magnetic flux is similarly described by three coupled RG equations. The fixed point structure and and the implicit solution of these equations is presented. For sufficiently strong attractive interaction new fixed points are found.
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