Oxidative polymerization of plant oils and lipids is poorly understood yet widely encountered. Oil oxidation is accelerated at high temperatures, typically above 110°C, where tri-acylglycerides are converted into toxic compounds and viscous deleterious polymers. Polymerization of mono-unsaturated oil (210°C, 3h, open to air) was investigated by comparing four similar sized molecules with different functional groups: oleic acid, methyl oleate, trans-7-tetradecene and stearic acid. Non-volatile products identified by NMR spectroscopy are minor ketones for saturated fatty acid (stearic acid), epoxides for acyl chains without acid groups (methyl oleate, tetradecane) and copious oligomerization, through ester cross-links, for acyl chains with acid and olefinic groups (oleic acid). Long range C-H coupling clearly shows ester (not ether) cross-links, contradicting long held beliefs. Chain fragmentation also occurs as revealed by species with methylene groups bonded to oxygen, -CH2-O-C(=O)-R. Large size (slow diffusion) of the first oligomer (trimer) formed by thermal oxidation of oleic acid, (representing hydrolyzed vegetable oil) was evidenced by DOSY (diffusion ordered spectroscopy). Since the first oligomers formed still have reactive groups (olefin, carboxylic acid), poly-ester formation is inevitable at longer oxidation times. Model oil reactions monitored by NMR spectroscopy are important for resolving the complex chemistry of vegetable oil polymerization.