Stationary spherical diffusion flames can be established with the help of a spherical burner in which fuel is supplied internally to a stationary porous sphere in microgravity. The most important parameter in this configuration is the mass flow rate through the sphere, which can be controlled independently and conveniently. Other relevant parameters are the Damkohler number, which is proportional to the ambient pressure and to the surface area of the sphere, the heat loss to the burner, and the fuel and oxidant Lewis numbers. In this study we examine the characteristics of burner-generated diffusion flames as a function of these parameters, with particular attention given to extinction conditions. It is shown that steady flames can be sustained in the vicinity of the sphere even at sufficiently low injection velocities and that extinction occurs when excessive reactant leakage through the reaction zone develops.