Hetero‐multifunctional poly(ethylene glycol‐co‐glycerol) random copolymers with multiple hydroxyl functionalities and a single terminal functionality have been prepared by copolymerization of ethylene oxide (EO) and ethoxy ethyl glycidyl ether (EEGE) with the use of a suitable initiator, introducing a protected amino group or a double bond, respectively. Acidic deprotection was used for removal of the acetal protecting groups in the chain, and the terminal amino group was regenerated by catalytic hydrogenation. A series of copolymers with narrow polydispersity was obtained, varying comonomer fractions from 3 to 67% and molecular weights in the range of 5 000–32 000 g · mol?1 (1.05 < < 1.25). Molecular and thermal characterization was carried out using 1H‐ and 13C NMR, SEC and differential scanning calorimetry (DSC).