In this study, quasilinear polyglycidols (PG)s with ultralow degree of branching (DB) could be synthesized through anionic polymerization of glycidol carried out in the presence of triethylborane (TEB). PGs with DB ≤ 0.10, and molar masses up to 40 kg mol-1 could be indeed obtained using mono- or trifunctional ammonium carboxylates as initiator and under slow monomer addition conditions. The synthesis of degradable PGs through ester linkages obtained by copolymerization of glycidol with anhydride is also described. PG-based amphiphilic di- and triblock quasilinear copolymers were also derived. The role played by TEB is discussed and a polymerization mechanism is proposed.