Synthesis via dehalogenative coupling due to thermal annealing is one of the most common routes of growing metal-organic and covalent polymer networks on catalytic metal surfaces. We present a computational approach taking into account both metal-coordinated and covalent C-C bonding interactions, which drive the self-assembly of tetrabrominated polyarene molecules into single-layer ordered and disordered nanostructures. The proposed coarse-grained lattice model is simulated using the Monte Carlo method. We investigate the annealing effect in ensembles of nearly and fully dehalogenated molecules, accordingly decreasing the concentration of dissociated (chemisorbed) halogen atoms, to account for the desorption process. The results suggest that dissociated halogens may be at least partially responsible for fragmentation of metal-organic networks on the Cu and Au surfaces. The simulations also show that fragmented covalent networks are mostly disordered or characterized by short-range glass-like order, but larger domains of these phases can be obtained after removing the split off Br atoms. We additionally examine the potential formation of fragments with a hybrid structure consisting of oligomer chains linked side-to-side by metal adatoms.