  The spectral moments of ensembles of sparse random block matrices are
analytically evaluated in the limit of large order. The structure of the sparse
matrix corresponds to the Erd\"os-Renyi random graph. The blocks are i.i.d.
random matrices of the classical ensembles GOE or GUE. The moments are
evaluated for finite or infinite dimension of the blocks. The correspondences
between sets of closed walks on trees and classes of irreducible partitions
studied in free probability together with functional relations are powerful
tools for analytic evaluation of the limiting moments. They are helpful to
identify probability laws for the blocks and limits of the parameters which
allow the evaluation of all the spectral moments and of the spectral density.
