  The Hurwitz complex continued fraction is a generalization of the nearest
integer continued fraction. In this paper we prove various results concerning
extremes of the modulus of Hurwitz complex continued fraction digits. This
includes a Poisson law and an extreme value law. The results are based on cusp
estimates of the invariant measure about which information is still limited. In
the process, we get several results concerning extremes of nearest integer
continued fractions as well.
