Long time black hole evaporation with bounded Hawking flux

A list of four rather general assumptions is presented, concerning allowed deformations of symmetries, asymptotics of space-time, restriction of its causal structure and behavior of the Hawking flux as measured by an asymptotic observer. Specifying them in a "natural" way, together with a few simplifying technical assumptions, leads to the prediction that due to the evaporation process a Schwarzschild black hole transforms continuously towards a remnant geometry. Picturesquely speaking, the celestial sphere evaporates into a celestial circle. As a byproduct the string inspired dilaton black hole is found to be an unstable fixed point of the evaporation evolution. Physical meaning and possible relaxations of the basic assumptions are discussed.