  In this paper, we discuss a method of constructing separable representations
of the $C^*$-algebras associated to strongly connected row-finite $k$-graphs
$\Lambda$. We begin by giving an alternative characterization of the
$\Lambda$-semibranching function systems introduced in an earlier paper, with
an eye towards constructing such representations that are faithful. Our new
characterization allows us to more easily check that examples satisfy certain
necessary and sufficient conditions. We present a variety of new examples
relying on this characterization. We then use some of these methods and a
direct limit procedure to construct a faithful separable representation for any
row-finite source-free $k$-graph.
