Hyperbranched polyglycerol (PG) is established as one of the few hyperbranched polymers that offer the possibility to control molecular weight up to Mn = 6000 g/mol. This work introduces a facile 2-step strategy that relies on the use of a low molecular weight PG (Mn = 500 and 1000 g/mol) as a macroinitiator for the slow addition of glycidol, permitting to overcome previous limitations concerning molecular weights and molecular weight control. A systematic investigation of the effect of the degree of deprotonation on the control of the polymerization reaction has been carried out. A series of hyperbranched PGs with molecular weights up to Mn = 24000 g/mol has been obtained under fully controlled conditions. The polydispersities of the samples prepared were in the range of 1.3 to 1.8. In summary, we present the first example of a synthetic strategy for a hyperbranched polymer that is now accessible over a broad range of molecular weights (300-24000 g/mol) without the ubiquitous problem of large polydispersities or the necessity for solid supports. In addition, the samples permitted a systematic study of the degree of branching DB of the hyperbranched PGs of elevated molecular weight. Values of DB = 0.60 to 0.63 were obtained, approximating the theoretical limit of 0.66 for slow monomer addition.