  We study the empirical spectral distribution (ESD) for complex n x n matrix
polynomials of degree k. We obtain exact formulae for the almost sure limit of
the ESD in two distinct scenarios: (1) n -> \infty with k constant and (2) k ->
\infty with n bounded by O(k^P) for some P>0. The main tools used are the
logarithmic potential of some measure related to the matrix polynomial, and
some classical estimates on the singular values of full random matrices with
i.i.d. entries.
