  We study purely atomic representations of C*-algebras associated to
row-finite and source-free higher-rank graphs. We describe when purely atomic
representations are unitarily equivalent and we give necessary and sufficient
conditions for a purely atomic representation to be irreducible in terms of the
associated projection valued measure. We also investigate the relationship
between purely atomic representations, monic representations and permutative
representations, and we describe when a purely atomic representation admits a
decomposition consisting of permutative representations.
