  In this paper we first give arguments supporting the idea that a B.T.Z black
hole can face a transplankian problem even when its mass is small. K.M.M
quantum theory is applied to the Hawking evaporation of the Schwarzchild and
B.T.Z black holes. Working in the physically safe quasi position
representation, we argue that the oscillating term present in a previous
analysis is removed so that actually one doesn't need an average procedure. We
expand the s wave function as the exponential of a series in the minimal length
of the new quantum theory. This reduces an infinite order differential equation
to a numerable set of finite order ones. We obtain the striking result that the
infinity of arbitrary constants induced by the order of the wave equation has
no physical meaning due to normalization. We finally construct gaussian wave
pacqets and study their trajectories. We suggest a quantitative description of
the non locality zone and its dependance on the K.M.M energy scale. Potential
incidences on unitarity are briefly evoqued.
