Glycidol as latent branching AB(2) monomer was used in combination with glycidyl ethers as linear AB comonomers for the preparation of hyperbranched random copolymers with controlled degree of polymerization (DPn = 42-72) and relatively low polydispersity (M-w/M-n < 1.7). Extending previous theoretical considerations, equations that permit to calculate the DB for AB(2)/AB copolymerizations under slow monomer addition conditions were derived. The degree of branching (DB) for the random copolymers of glycidol and allyl glycidyl ether (AGE) as well as phenyl glycidyl ether (PGE) was controlled by the comonomer ratio (DB = 9%-58%). Furthermore, comparable block copolymers of glycidol and AGE, i.e., multiarm star polymers, have been prepared by sequential addition of the monomers. Thermal behavior of all materials has been investigated with respect to copolymer composition. Furthermore, reactions of the random glycidol/AGE copolymers have been developed: (i) cleavage of the allyl groups, leading to linear 1,3-glycerol units bearing primary hydroxy groups; (ii) dihydroxylation of the double bond, leading to hyperbranched polyglycerols with enhanced DB; and (iii) hydroformylation with subsequent reductive amination, making use of the orthogonality of the OH and allyl functionalities.