Vapor-liquid equilibrium data for systems of hyperbranched polymer (HBP) and carbon dioxide are reported for temperatures of 285-455 K and pressures up to 13 MPa. The bubble-point pressures Of (CO2 + hyperbranched polyester) and of (CO2 + hyperbranched polyglycerol + CH3OH) samples with fixed compositions were measured using a Cailletet apparatus. The system (CO2 + polyglycerol + CH3OH) also exhibits a liquid-liquid phase split characterized by lower critical solution temperatures. For this system cloud point curves and vapor-liquid-liquid bubble-point curves were also measured. Moreover, a thermodynamic model has been developed for HBP mixtures in the framework of the perturbed-chain polar statistical association fluid theory (PCP-SAFT) equation of state accounting for branching effects. There is no additional binary interaction parameter introduced along with the branching contributions to the model. Although the miscibility gap in the system (CO2 + polyglycerol + CH3OH) is not predicted by the model, PCP-SAFT including branching effects gives a good representation of the bubble-point curves of this system at temperatures lower than the lower solution temperature (LST).