PACS 72.80. Le, 82.35.Np The temperature dependences of the resistance, current-voltage characteristics, and dielectric spectra of composites based on polypropylene and fillers made of micro-and nano-sized carbon particles have been studied. A reduction in the average size of conducting filler particles is found to decrease the resistivity magnitude, to shift the posistor section in the current-voltage characteristics toward lower electric fields and larger currents, and to increase the low-frequency dielectric permittivity of the researched composites. It is shown that these "size"effects can be explained by a growth of the effective fraction of the volume occupied by the conducting filler owing to the emergence of interfacial boundary layers in the polypropylene matrix. The electric properties of the layers differ from those for bulk polyethylene, and charge carriers can move in them. In other words, a change in the size of carbon particles gives rise to changes in the specific area and the effective fraction of the conducting filler.K e y w o r d s: composite, carbon filler, conductivity, dielectric permittivity, interphase layer.