This paper describes the synthesis of a new cyclic carbonate AB(2) type monomer, 5-{3-[(2-hydroxyethyl)thio]propoxy}-1,3-dioxan-2-one (5), and its application for preparation of hyperbranched polymers. In addition, a linear analogue of poly(5) was prepared, and the structures were compared by means of C-13 NMR. Ring-opening polymerization of 5 leads to a polymer containing solely primary hydroxyl groups. The influence of the catalyst and reaction conditions used for the polymerization on the structure of the polymer is discussed. Moreover, the presence of glycerol and carbonate residues in the repeating unit makes the polymer potentially biodegradable and biocompatible-promising material for drug delivery. The application of free-radical addition of mercaptoethanol to allyl bonds simplified the synthetic route and allowed the use of hyperbranched polymer (HBP) with thioether groups as potential host molecules for transition metal cations (Cr, Rh) complexation.