AF-embeddability of 2-graph algebras and quasidiagonality of k-graph algebras

We characterise quasidiagonality of the C*-algebra of a cofinal k-graph in terms of an algebraic condition involving the coordinate matrices of the graph. This result covers all simple k-graph C*-algebras. In the special case of cofinal 2-graphs we further prove that AF-embeddability, quasidiagonality and stable finiteness of the 2-graph algebra are all equivalent.