The realization of molecule-based miniature devices with advanced functions requires the development of new and efficient approaches for combining molecular building blocks into desired functional structures, ideally with these structures supported on suitable substrates 1-4. Supramolecular aggregation occurs spontaneously and can lead to controlled structures if selective and directional non-covalent interactions are exploited. But such selective supramolecular assembly has yielded almost exclusively crystals or dissolved structures 5; the self-assembly of absorbed molecules into larger structures 6-8, in contrast, has not yet been directed by controlling selective intermolecular interactions. Here we report the formation of surface-supported supramolecular structures whose size and aggregation pattern are rationally controlled by tuning the non-covalent interactions between individual absorbed molecules. Using low-temperature scanning tunnelling microscopy, we show that substituted porphyrin molecules adsorbed on a gold surface form monomers, trimers, tetramers or extended wire-like structures. We find that each structure corresponds in a predictable fashion to the geometric and chemical nature of the porphyrin substituents that mediate the interactions between individual adsorbed molecules. Our findings suggest that careful placement of functional groups that are able to participate in directed non-covalent interactions will allow the rational design and construction of a wide range of supramolecular architectures absorbed to surfaces.