A fundamental question in origin-of-life studies and astrochemistry concerns the actual processes that initiate the formation of reactive monomers and their oligomerization. Answers lie partly in the accurate description of reaction mechanisms compatible with environments plausible on early Earth as well as cosmological scenarios in planetary factories. Here we show in detail that reactions of urea-as archetypal prebiotic substance-and reactive carbonyls-exemplified by glyoxal-lead to a vast repertoire of oligomers, in which different five- and six-membered non-aromatic heterocycles self-assemble and insert into chains or dendritic-like structures with masses up to 1000 Da. Such regular patterns have been interpreted by experimental and computational methods. A salient conclusion is that such processes most likely occur through SN-type mechanisms on hydrated or protonated species. Remarkably, such supramolecular oligomeric mixtures can be easily isolated from organic solvents, thus opening the door to the generation of novel urea-containing polymers with potential applications in materials chemistry and beyond.