A detailed structural analysis of the surface supported self-assembly of terphenyl-4,4′′-dicarbonitrile molecules (NC−Ph3−CN) linked by Co adatoms on Ag(111) reveals different surface patterns depending on the constraints applied to the system. Without constraints, i.e., sufficient mobility and absence of space limitations at the surface, extended regular honeycomb nanomeshes are formed. On the basis of high-resolution scanning tunneling microscopy images, an atomistic model is derived showing the crystallographic orientation of the molecules and a commensurate alignment of the honeycomb networks, which exist in two rotational domains on the Ag(111) atomic lattice. For Co deficiency, an additional star-like Co-directed motif has been identified, and fully disordered networks are present if space limitations are imposed. In these cases, nodal motifs exist showing between 3- and 6-fold coordination of Co centers.