Glycidol represents a latent cyclic AB(2)-type monomer that can be polymerized in a ring-opening multibranching polymerization (ROMBP). Hyperbranched aliphatic polyethers with controlled molecular weights and narrow molecular weight distribution have been prepared via anionic polymerization of glycidol with rapid cation-exchange equilibrium. 1,1,1-Tris(hydroxymethyl)propane (TMP) was partially deprotonated (10%) and used as initiator for the anionic polymerization carried out under slow addition conditions to minimize polymerization without initiator as well as cyclization, C-13 NMR spectra were employed to assess the degree of branching (DB), which was in the range 0.53-0.59. C-13 NMR, MALDI-TOF mass spectrometry, vapor pressure osmometry (VPO), and GPC were used to characterize molecular weights and polydispersities of the polyols formed, showing good agreement. DP, for the polymers prepared was in the range 15-83 ((M) over bar(n) = 1250-6500), and (M) over bar(w)/(M) over bar(n) obtained was 1.13-1.47, being exceptionally low for hyperbranched polymers. MALDI-TOF spectra evidenced complete attachment of the hyperbranched structures to the TMP initiator and the absence of macrocyclics as well as hyperbranched macromolecules without initiator, due to the slow addition. The hyperbranched polyethers prepared showed T-g's between -20 and -26 degrees C.