Molecular self-assembly based on the spontaneous arrangement of simple, functional molecules on atomically flat surfaces has been recognized, in the past decades, as an extremely useful tool for the rational fabrication of one-atom-thick nanomaterials, with potential application in heterogeneous catalysis, selective adsorption, and sensing. The physicochemical properties of such supramolecular constructs are determined mainly by the proper choice of chemical interactions cementing their components. Particularly suitable for this purpose are directional, reversible ligand → metal coordinate bonds. In this contribution, we present the results of coarse-grained Monte Carlo (MC) computer simulations performed on the family of isomeric, starshaped molecular building blocks, coadsorbed with low-coordinated metal atoms on the triangular lattice. We have found that depending on the position of active centers (functional groups) attached to the terminal segments of investigated molecules, the bottom-up fabrication of complex metal-organic overlayers, like nanoporous networks, nonregular tessellations, and ladder-like chains, is possible. The obtained patterns are described and classified according to their geometrical properties. The herein presented theoretical predictions can be especially helpful for scanning tunneling microscopy (STM) experimentalists interested in the rational designing of novel surface-supported metal-organic architectures with an unusual morphology and tunable physicochemical properties.