  Kaluza-Klein reduction of 3D gravity with minimal scalars leads to 2D
dilaton-Maxwell gravity with dilaton coupled scalars. Evaluating the one-loop
effective action for dilaton coupled scalars in large $N$ and s-wave
approximation we apply it to study quantum evolution of BTZ black hole. It is
shown that quantum-corrected BTZ BH may evaporate or else anti-evaporate
similarly to 4D Nariai BH as is observed by Bousso and Hawking. Instable higher
modes in the spectrum indicate also the possibility of proliferation of BTZ BH.
