The transport layer concept is employed to derive an algebraic equation for the premixed flame (PF) are shape in a tribrachial or triple flame near a cold wall. The PF are shape degenerates from a triple flame (when the flame tip is far from the cold, porous surface located at the exit plane) into a "flame nub" (when the flame tip is close to the exit plane). The dependence of the PF are shape on the heat losses to the upstream wall enters through the upstream quench-zone temperature profile contained in the modified Damkohler number, d, given by Eq. 13. This progressive degradation of the triple flame structure is consistent with all available numerical solutions of the equations of combustion theory. It is also consistent with experimental observations in opposed-flow flame spread and for attached burner (jet) flames.