Electrical conductivity and rheological measurements were performed to study the influence of particle dimension on the formation of the filler network in a polymer melt. For the fillers carbon nanoparticles with one, two, three or fractal (2 < d ≤ 3) dimensions were compared. For this purpose, multi-walled carbon nanotubes (CNT), graphite nanoplates (GNP) and carbon black (CB) were incorporated in a polycarbonate matrix. The insulator-conductor transition of the different composites was studied by dielectric spectroscopy. The electrical conductivity in the melt was measured in a rheo-electrical setup with the electrical field perpendicular to the shear plane and in the shear plane under steady shear conditions as well as in the quiescent melt. During a weak shear flow a breakdown of the electrical conductivity and steady state values of conductivity and viscosity were observed for all filler systems. This general feature can be explained by the interplay of destruction and built up of the filler network. After stopping the shear flow a reorganization of the filler network occurs, which leads to an increase in electrical conductivity. This increase is slower and less complete for GNP and GNP/CB as compared to CB and CNT. For fillers with platelet geometry (GNP and GNP/CB composites) the conductivity perpendicular to the shear plane was found to be higher than in shear direction. This anisotropic conductivity is preserved during recovery of the filler network in the quiescent melt, whereas the CB composites show an equalization of the conductivities of the two directions. This is explained by incomplete reorientation of GNP due to slow rotational diffusion or sterically hindered orientation and the faster translational diffusion for CB. In the case of CNT the CNT orientation is suppressed by agglomeration.