Prebiotic formation of triazines from urea was studied using density functional theory methods with the aim of understanding some of the neutral precursors that can lead to a mixture of triazines. The proposed mechanisms are based on free radical routes without solvent requirements that are appropriate for prebiotic scenarios occurring under highly non-equilibrium conditions. These include spark discharge or ultraviolet driven reactions taking place on or within low temperature ice or reactions simulated by meteoritic impact on organic surfaces on Titan and possibly early Earth. The ice increases radical lifetimes while the impact events produce sufficient heat to generate useful free radical densities in the impact zones. The mechanisms proceed through relatively low energy barriers. The pathways predict that biuret is a precursor for cyanuric acid, and guanylurea is a precursor for both melamine and ammeline. Based on the predicted precursors of the triazines, the established mechanisms provide theoretical support for previous thermal synthesis of the triazines from urea and biuret.