  We complete the analysis started in [arXiv:0804.0198] of the Hawking
radiation calculated by means of anomaly techniques. We concentrate on a static
radially symmetric BH, reduced to two dimensions. We compare the two methods
used to derive the integrated Hawking radiation, based on the trace and
diffeomorphism anomaly, respectively, and show that they can be reduced to the
same basic elements. We then concentrate on higher moments of the Hawking
radiation and on higher spin currents, and show that, similarly to trace
anomalies, also diffeomorphism anomalies are absent from the conservation laws
of higher spin currents. We show that the predictivity of the method is due to
the $W_\infty$ current algebra underlying the effective model that describes
matter around the black hole.
