Process comprising the steps of: a) heating for a time of at least 10 minutes a starting mixture of one or more triglycerides containing saturated dicarboxylic acids, obtaining an intermediate mixture comprising said triglycerides in condensed form and one or more free dicarboxylic acids (condensation step); b) esterifying said intermediate mixture with monohydric alcohols, obtaining a reaction product comprising one or more oligomeric structures and one or more diesters of dicarboxylic acids (esterification step); c) separating said diesters of dicarboxylic acids from said reaction product, obtaining a final mixture of triglycerides comprising one or more oligomeric structures (separation step), wherein the said oligomeric structures have the following structure: R 4 -[O-C(O)-R 1 -C(O)-O-CH 2 -CH(OR 2 )-CH 2 ] n -O-R 3 in which R 1 is selected from C 2 -C 22 alkylenes, R 2 is selected from one or more of the following groups consisting of C 6 -C 24 dicarboxylic acid residues and C 6 -C 24 monocarboxylic acid residues, R 3 is selected from one or more of the following groups consisting of H, C 6 -C 24 dicarboxylic acid residues and C 6 -C 24 monocarboxylic acid residues, R 4 is an alkyl group, n is a whole number equal to or greater than 2, the said C 6 -C 24 dicarboxylic acids of R 2 and R 3 being esterified with monoalcohols and the said mixture of triglycerides having a Number Average Molecular Weight (Mn) of between 800 and 10,000 Da. a) heating for a time of at least 10 minutes a starting mixture of one or more triglycerides containing saturated dicarboxylic acids, obtaining an intermediate mixture comprising said triglycerides in condensed form and one or more free dicarboxylic acids (condensation step); b) esterifying said intermediate mixture with monohydric alcohols, obtaining a reaction product comprising one or more oligomeric structures and one or more diesters of dicarboxylic acids (esterification step); c) separating said diesters of dicarboxylic acids from said reaction product, obtaining a final mixture of triglycerides comprising one or more oligomeric structures (separation step), wherein the said oligomeric structures have the following structure: R 4 -[O-C(O)-R 1 -C(O)-O-CH 2 -CH(OR 2 )-CH 2 ] n -O-R 3 in which R 1 is selected from C 2 -C 22 alkylenes, R 2 is selected from one or more of the following groups consisting of C 6 -C 24 dicarboxylic acid residues and C 6 -C 24 monocarboxylic acid residues, R 3 is selected from one or more of the following groups consisting of H, C 6 -C 24 dicarboxylic acid residues and C 6 -C 24 monocarboxylic acid residues, R 4 is an alkyl group, n is a whole number equal to or greater than 2, the said C 6 -C 24 dicarboxylic acids of R 2 and R 3 being esterified with monoalcohols and the said mixture of triglycerides having a Number Average Molecular Weight (Mn) of between 800 and 10,000 Da. R 1 is selected from C 2 -C 22 alkylenes, R 2 is selected from one or more of the following groups consisting of C 6 -C 24 dicarboxylic acid residues and C 6 -C 24 monocarboxylic acid residues, R 3 is selected from one or more of the following groups consisting of H, C 6 -C 24 dicarboxylic acid residues and C 6 -C 24 monocarboxylic acid residues, R 4 is an alkyl group, n is a whole number equal to or greater than 2, the said C 6 -C 24 dicarboxylic acids of R 2 and R 3 being esterified with monoalcohols and the said mixture of triglycerides having a Number Average Molecular Weight (Mn) of between 800 and 10,000 Da. <EOS>