Species likely to be present in methylaluminoxane (MAO) are studied via dispersion-corrected DFT, which we show is able to accurately predict thermochemical parameters for the dimerization of trimethylaluminum (TMA). Both cage-like, (AlOMe)(n),(c), and TMA-bound nanotubes, (AlOMe)(n,t) (AlMe3)(m), are found to be important components of MAO. The most stable structures have aluminum/oxygen atoms in environments whose average hybridization approaches sp(3)/sp(2). The (AlOMe)(n),(t) (AlMe3)m isomers with the lowest free energies possess Al-mu-MeAl bonds. At 298 K a novel T-d-(AlOMe)(16),c oligomer is one of the most stable structures among the six stoichiometries with the lowest free energies: (AlOMe)(20,c) (AlMe3)(2), T-d-(AlOMe)(16,c), (AlOMe)(18,c), (AlOMe)(20,c) (AlMe3), (AlOMe)(10,t) (AlMe3)(4), and (AlOMe)(20,c). As the temperature rises, the abundance of (AlOMe)(n,t) (AlMe3)(m) decreases, and that of (AlOMe)(n,c) increases. Because the former are expected to be precursors for the active species in polymerization, this may in part be the reason why the cocatalytic activity of MAO decreases at higher temperatures.