Synthesis of fully hydrophilic star-shaped macromolecules with different kinds of arms (A(x)B(y)C(z)) based on polyglycidol (PGL, A(x)) and poly(ethylene oxide) (PEO, C(z)) arms and diepoxy compounds (diglycidyl ethers of ethylene glycol (DGEG) or neopentyl glycol (DGNG) in the core, B(y)) forming the core is described. Precursors of arms were prepared by polymerization of glycidol with protected -OH groups. The first-generation stars were formed in the series of consecutive-parallel reactions of arms A(x) with diepoxy compounds (B). These first-generation stars (A(x)B(y)), having approximately O-, Mt+ groups on the cores, were used as multianionic initiators for the second generation of arms (C(z)) built by polymerization of ethylene oxide. The products with M(n) up to 10(5) and having up to approximately 40 arms were obtained. The number of arms (f) was determined by direct measurements of M(n) of the first-generation stars (M(n) of arms A(x) is known), compared with f calculated from the branching index g, determined from R(g) measured with size-exclusion chromatography (SEC) triple detection with TriSEC software. The progress of the star formation was monitored by 1H NMR and SEC. These novel water-soluble stars, having a large number of hydroxyl groups, both at the ends of PEO arms as well as within the PGL arms, can be functionalized and further used for attaching compounds of interest. This approach opens, therefore, a new way of "multiPEGylation".