The structure and extinction of a diffusion flame stabilized by a spherical porous burner, and attached to the burner, was analyzed by activation energy asymptotics. The extinction state was identified by the smallest Damkohler number, representing the weakest burning intensity, at which a flame exists. Four limiting flames, based on a fuel/air flame, but with different flow direction and inert distribution, were used to study the effects of various controlling parameters. For the attached flame, the burning characteristics and extinction state were controlled by the mass fraction of the reactant supplied from the burner (lean reactant), and the flame behaves like a premixed flame with a lean reactant. This is consistent with the premixed flame regime introduced by Linan. With reduced Damkohler number (Da), or mass flow rate (m), the reaction becomes weaker, the leakage of the burner reactant increases, and there exists a minimum Da or m below which the flame extinguishes. Comparison of the four flames reveals that all four flames extinguish at the same fuel consumption rate when other conditions are the same. As to the effects of Lewis numbers, the flame is stronger and more difficult to extinguish when either the Lewis number of the reactant supplied from the burner is increased or the Lewis number of the reactant in the ambient is decreased. When the size of the burner is reduced, the flame reaches the burner at a smaller mass flow rate with extinction occurring also at a smaller flow rate. There exists a smallest burner size below which the flame will extinguish before reaching the burner. (C) 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.