Graphene oxide (GO)—branched poly(ethyleneimine) (BPEI) hydrated mixtures were studied by means of fully atomistic molecular dynamics simulations to assess the effects of the size of polymers and the composition on the morphology of the complexes, the energetics of the systems and the dynamics of water and ions within composites. The presence of cationic polymers of both generations hindered the formation of stacked GO conformations, leading to a disordered porous structure. The smaller polymer was found to be more efficient at separating the GO flakes due to its more efficient packing. The variation in the relative content of the polymeric and the GO moieties provided indications for the existence of an optimal composition in which interaction between the two components was more favorable, implying more stable structures. The large number of hydrogen-bonding donors afforded by the branched molecules resulted in a preferential association with water and hindered its access to the surface of the GO flakes, particularly in polymer-rich systems. The mapping of water translational dynamics revealed the existence of populations with distinctly different mobilities, depending upon the state of their association. The average rate of water transport was found to depend sensitively on the mobility of the freely to move molecules, which was varied strongly with composition. The rate of ionic transport was found to be very limited below a threshold in terms of polymer content. Both, water diffusivity and ionic transport were enhanced in the systems with the larger branched polymers, particularly with a lower polymer content, due to the higher availability of free volume for the respective moieties. The detail afforded in the present work provides a new insight for the fabrication of BPEI/GO composites with a controlled microstructure, enhanced stability and adjustable water transport and ionic mobility.