A simple model of radiating diffusion flames considered by Kavousanakis et al. (2013) [1] is extended to two spatial dimensions. A large variety of stationary spatially localized states representing the breakup of the flame front near extinction is computed using numerical continuation. These states are organized by a global bifurcation in space that takes place at a particular value of the Damkohler number and their existence is consistent with current understanding of spatial localization in driven dissipative systems. (C) 2016 The Combustion Institute. Published by Elsevier Inc. All rights reserved.