Directing the self-assembly of organic molecules towards low-dimensional superstructures has been an attractive method of fabrication of functional materials with programmable architecture. In this contribution, using theoretical modeling, we demonstrate how fine tuning of directional intermolecular interactions which are encoded in a simple organic building block allows for the creation of surface-confined assemblies with largely diversified morphology. To that end the self-assembly of a model tripod-shaped molecule adsorbed on a triangular lattice was simulated using the canonical ensemble Monte Carlo method. The simulations were performed for flat, rigid building blocks built of four discrete segments (core plus three arm segments) and equipped with adjustable peripheral interaction centers providing directional intermolecular bonds. The simulated results revealed that changes in the directionality of interactions imposed on the centers are responsible for the emergence of different molecular structures including ordered porous networks, chain and ladder structures and chiral patterns. The obtained assemblies were analyzed and classified with respect to their structural and energetic properties. Our theoretical investigations showed that small changes in the position of the outer interaction centers in a tripod functional molecule can have dramatic effect on the morphology of the resulting 2D structures. On the other hand, these findings can be helpful in predicting the self-assembly of organic tripod molecules with the different interaction patterns discussed in this study. This information, can be relevant, for example, to synthetic chemists seeking for an optimal building block able to self-assembly into a 2D superstructure with predefined properties.