This talk discusses the notion of monic representations for $C$*-algebras associated to finite higher-rank graphs without sources, generalizing a concept first defined by D. Dutkay and P. Jorgensen for representations of Cuntz algebras. Monic representations are those that, when restricted to the commutative $C$-algebra of continuous functions on the infinite path space associated to the graph, admit a cyclic vector. We connect these representations to the $\Lambda$-semibranching systems studied in earlier joint work with C. Farsi, E. Gillaspy, and S. Kang. The results discussed are based on joint work with C. Farsi, E. Gillaspy, S. Kang, and P. Jorgensen.