An original strategy is proposed to easily design functional materials from poly(glycerol succinate) (PGS). This approach consists in the introduction of an epoxidized functional agent during the polyesterification between the glycerol and succinic acid. In order to model the effect of this epoxide group on the polymerization process and its resulting hyperbranched architecture, the butyl glycidyl ether (BGE) has been selected as comonomer agent. The theoretical potential reactions have been confronted with the topological units revealed by 2D NMR correlations. The regioselectivity against the primary alcohol and the stoichiometric balance of the system have been modified in situ by the kinetic control of parallel reactions. This had the effect to delay the gelation and increase the polyesterification conversion. The resulting hyperbranched polymers (HBPs) obtained just after gelation exhibit a temperature of glass transition (T-g) of-3.9 degrees C for PGS and -16.1 degrees C for poly(glycerol-succinate-co-butyl glycidyl ether) (PGS-co-BGE). This difference was explained by the BGE butyl tails effect which plays the role of dynamic spacer between the polymer chains during the relaxation process. The relaxation processes were investigated by the computation of the effective activation energy (E-a) through the T-g using the advanced isoconversional method and by the estimation of the beta-relaxation activation energy (E-beta) by means of annealing experiments. The variation of Ea and E-beta values was discussed in terms of competition between the cooperative/noncooperative segment motions and the hindrance effect of the hydrogen-bonded network. The dynamic behavior of this system can be potentially generalizable to all the plastic glass containing a critical amount of secondary interactions.