  We study asymptotics of the Itzykson-Zuber integrals in the scaling when one
of the matrices has a small rank compared to the full rank. We show that the
result is basically the same as in the case when one of the matrices has a
fixed rank. In this way we extend the recent results of Guionnet and Maida who
showed that for a latter scaling the Itzykson-Zuber integral is given in terms
of the Voiculescu's R-transform of the full rank matrix.
