  Quantum back reaction due to $N$ massless fields may be worked out to a
considerable detail in a variant of integrable dilaton gravity model in two
dimensions. It is shown that there exists a critical mass of collapsing object
of order $\hbar N \times$ (cosmological constant)$^{1/2}$, above which the end
point of Hawking evaporation is two disconnected remnants of infinite extent,
each separated by a mouth from the outside region. Deep inside the mouth there
is a universal flux of radiation in all directions, in a form different from
Hawking radiation. Below the critical mass no remnant is left behind, implying
complete Hawking evaporation or even showing no sign of Hawking radiation.
Existence of infinitely many static states of quantum nature is also
demonstrated in this model.
