  This paper is a direct continuation of "Functional analysis behind a Family
of Multidimensional Continued Fractions: Part I," in which we started the
exploration of the functional analysis behind the transfer operators for
triangle partition maps, a family that includes many, if not most, well-known
multidimensional continued fraction algorithms. This allows us now to find
eigenfunctions of eigenvalue 1 for transfer operators associated with select
triangle partition maps on specified Banach spaces. We proceed to prove that
the transfer operators, viewed as acting on one-dimensional families of Hilbert
spaces, associated with select triangle partition maps are nuclear of trace
class zero. We finish by deriving Gauss-Kuzmin distributions associated with
select triangle partition maps.
