The adsorption of the weak and branched polyelectrolyte polyethylenimine (PEI) on planar, uncharged graphite surfaces is investigated with the atomic force microscope (AFM). The high lateral resolution of the AFM allows for the observation of single molecules adsorbed to the surface from diluted solutions. Different adsorption structures were found in dependence of the pH value of the solution and the incubation time of the adsorption process. Patterns of individual PEI molecules are due to repulsive interactions. These interactions result in a main intermolecular distance and highly ordered stringlike structures. Equal intermolecular distances for all pH values reveal the ability of the PEI molecules to adjust their charge density. Dipolar interactions explain the high ordering of the molecules. Furthermore, the superimposing influence of the hexagonal graphite lattice can be observed for long adsorption times.