Fully atomistic molecular dynamics simulations were employed in order to examine in detail the self assembly characteristics and the complexation behavior of the anticancer drug doxorubicin with PEGylated hyperbranched polyesters in an aqueous environment. We have examined two variants of the polymeric compound by altering the length of the hydrophilic poly(ethylene glycol) arms attached to the hydrophobic hyperbranched core. By comparing the clustering properties of the drug molecules in a polymer-free system to those in the polymer-containing models, we were able to assess the effects related to the presence and to the structural features of the polymer moiety. In addition, we have distinguished the effects associated with the neutral and protonated drug molecules separately. It was found that, in the presence of the polymeric material, the drug molecules formed clusters preferentially close to the polymer's periphery, the characteristics of which depended on the structural details of the polymeric host and on the charge of the drug molecules. Hydrogen bonding was found to contribute to the polymer/drug complexation, with the nature of the prevailing donor/acceptor pairs depending on the charge of the drug. Dynamic analysis of the drugs' motion revealed that in the polymer-containing systems the drug molecules experienced a larger degree of confinement within the formed clusters compared to that describing their polymer-free analogues, while the structural coherence of the clusters was found to be more persistent in the system with the larger poly(ethylene glycol) arms. The results described in this work, through the monitoring of both static and dynamic aspects of the self-association and the complexation behavior of the neutral and charged molecules of doxorubicin with the polymeric host, may help toward the elucidation of the key parameters that are involved in the formation of effective polymer-based carriers for drug molecules of the anthracycline family used in cancer chemotherapy.