  Formulae of Plancherel-Rotach type are established for the average
characteristic polynomials of certain Hermitian products of rectangular Ginibre
random matrices on the region of zeros. These polynomials form a general class
of multiple orthogonal hypergeometric polynomials generalizing the classical
Laguerre polynomials. The proofs are based on a multivariate version of the
complex method of saddle points. After suitable rescaling the asymptotic zero
distributions for the polynomials are studied and shown to coincide with the
Fuss-Catalan distributions. Moreover, introducing appropriate coordinates,
elementary and explicit characterizations are derived for the densities as well
as for the distribution functions of the Fuss-Catalan distributions of general
order.
