We explore by means of molecular dynamics (MD) simulations mixtures of graphene with hyperbranched polyesters (Boltorn) of two different pseudogenerations in a wide range of temperatures. Static and dynamic features of the polymeric component are probed in order to assess the effects of the presence of graphene in the polymers behavior, while we also examine the structural rearrangement of the graphene sheets in the presence of a noncrystallizable highly branched polymeric component. Our results show that graphene platelets are forming stacks comprised by a small number of flakes (typically 23) which are dispersed within the polymeric matrix. The characteristics of the spatial arrangement of the graphene planes and that of the formed clusters (including their relative orientation) depend sensitively on the temperature and on the size of the hyperbranched component. From the dynamic point of view, a significant slowing down is detected both in local and in global polymer dynamics in composite systems. The strong dynamic slowing down is accompanied by the occurrence of a glass-like transition at a considerably higher temperature compared to that characterizing the respective pristine polymer systems. We believe that the results reported in the present study capture also generic characteristics of the behavior of such materials and therefore could be exploited for a better control of the mechanical and thermal characteristics of hyperbranched polymer/graphene systems in a more general aspect.