Results are presented of ab initio studies at levels MP2(full)/6-31G* and MP2(full)/6-311G* of the hydrolysis of trimethylaluminum (TMA, 1) to dimethylaluminumhydroxide (DMAH, 2) and of the intramolecular 1,2-elimination of CH4 from 2 itself to form methylaluminumoxide 3, from its dimeric aggregate 4 to form hydroxytrimethyldialuminoxane 5 and dimethylcyclodialuminoxane 6, and from its TMA aggregate 7 to form 8 and/or 9, the cyclic and open isomers of tetramethyldialuminoxane, respectively. Each methane elimination creates one new Lewis acid site, and dimethylether is used as a model oxygen-donor molecule to assess the most important effects of product stabilization by Lewis donor coordination. It is found that the irreversible formation of aggregate 4 (ΔG298 = -29.2 kcal/mol) is about three times more exergonic than the reversible formation of aggregate 7 (ΔG298 = -9.9 kcal/mol), that the reaction free enthalpies for the formations of 5 (ΔG298 = -9.0 kcal/mol) and 6 (ΔG298 = -18.8 kcal/mol) both are predicted to be quite clearly exergonic, and that there is a significant thermodynamic preference (ΔG298 = -7.2 kcal/mol) for the formation of 6 over ring-opening of 5 to hydroxytrimethyldialuminoxane 10. The mechanism for oligomerization is discussed based on the bonding properties of dimeric aggregates and involves the homologation of HO-free aluminoxane with DMAH (i.e., 9 to 13), and any initially formed hydroxydialuminoxane 10 is easily capped to trialuminoxane 13. Our studies are consistent with and provide support for Sinn's proposal for the formation of oligoaluminoxanes, and in addition, the results point to the crucial role played by the kinetic stability of 5 and the possibility to form cyclodialuminoxane 6. Dialuminoxanes 9 and 10 are reversed-polarity heterocumulenes, and intramolecular O→Al dative bonding competes successfully with Al complexation by Lewis donors. Intramolecular O→Al dative bonding is impeded in cyclodialuminoxane 6, and the dicoordinate oxygen in 6 is a strong Lewis donor. Ethylene polymerization catalysts contain highly oxophilic transition metals, and our studies suggest that these transition metal catalysts should discriminate strongly in favor of cycloaluminoxane-O donors even if these are present only in small concentrations in the methylaluminoxane (MAO) cocatalyst.