Highly functional, highly branched or hyperbranched polyesters, the production thereof and the use of the same

A high functionality, highly branched or hyperbranched polyester produced by a process comprising an acid catalyzed reaction of:

• (1) at least one aliphatic, cycloaliphatic, araliphatic or aromatic dicarboxylic acid (A2);
• and
• (2) at least one aliphatic, cycloaliphatic, araliphatic or aromatic diol (B2);
• with
• (3A) at least one aliphatic, cylcoaliphatic, araliphatic or aromatic polyol (Cx) having three or more hydroxyl groups;
• and
• (4) an optional functionalized building block (E);
• and
• (5) an optional α, β-unsaturated carboxylic acid (F),
• wherein the acid catalyzed reaction is carried out in the presence of at least one acidic catalyst, with the proviso that said acidic catalyst is not an enzyme,
• wherein a molar ratio of hydroxyl groups to carboxylic acid groups is from 5:1 to 1:5,
• wherein the polyester has a number average molecular weight of at least 500 g/mol and a polydispersity index of from 1.2 to 10,
• wherein the polyester has a degree of branching of from 10% to 99.9%, and
• wherein the polyester has a glass transition temperature (Tg) of from -40° C. to 100° C. as measured by differential scanning calorimetry (DSC) in accordance with ASTM 3418/82.