Self-assembly of star-shaped organic molecules on solid surfaces provides an effective approach to construct 2D functional nanostructures such as supramolecular networks with programmable architecture and functions. As it has been often observed experimentally, small changes in geometry and functionality of a building-block can directly influence the morphology and stability of the resulting two-dimensional molecular assemblies. In this contribution, we used the Monte Carlo simulation method in the Canonical Ensemble to explore the effect of shape and intramolecular distribution of interaction centers withina model cross-shaped building-block on the thermal stability of the resulting low-dimensional chiral structures. Specifically, for the cruciform molecular units we calculated heat capacities as a function of temperature and linked the position of the corresponding peak maxima with the structural parameters of the molecules. The obtained results indicate, that the heat capacities and the phase behaviour of the studied systems strongly depend on the properties of the building molecule, such as the number and position of interaction centers and molecular symmetry. Theinsights from this study can be helpful indesigning molecular architectonics on solid surfaces, especially when building blocks such as porphyrinsand phthalocyanines are at play. (C) 2016 Elsevier B. V. All rights reserved.