Copolymerization of established epoxide monomers with glycidol (G) is a key reaction to prepare branched or hyperbranched polyethers. The kinetics of the multibranching anionic ring-opening copolymerization of glycidol (a cyclic latent AB(2) monomer) with ethylene oxide (EO), propylene oxide (PO), and 1,2-butylene oxide (BO; cyclic latent AB monomers), respectively, in dimethyl sulfoxide was studied. Online H-1 NMR spectroscopy was employed for in situ monitoring of the individual monomer consumption during the entire course of the statistical copolymerization. Varying the counterion, both the cesium alkoxide and potassium alkoxide initiated copolymerization were studied and compared. From the individual monomer consumption, reactivity ratios were calculated. The reactivity ratio of the alkylene oxides decreases from 0.44 to 0.11 with increasing alkyl chain length on going from EO to BO. Unexpectedly, glycidol was found to exhibit a higher reactivity ratio in each copolymerization, with reactivity ratios ranging from 2.34 (with EO) to 7.94 (copolymerization with BO). Different counterions had an impact on absolute reaction rates, however, relative monomer reactivities remained unchanged. The reactivity ratios determine both the molecular weight distribution and the topology as well as the degree of branching (DB) of the respective branched copolymers, implying a change from a hyperbranched random copolymer (glycidol/EO) to a multiarm star structure with increasing side chain length of the alkylene comonomer.