The influence of the average surface area of different graphene nanoplatelets (GNP) on the thermo-electrical behaviour, associated with Joule heating, and the attenuation of electromagnetic signals of epoxy composites has been studied, analysing the effect of the morphology obtained as a function of the dispersion time by ultrasonication and the GNP content added. Gravity moulding was used as the first stage in the scaling-up, oriented to the industrial manufacture of multilayer coatings, observing a preferential self-orientation of nanoparticles and, in several conditions, a self-stratification too. The increase of sonication time during the GNP dispersion provides a decrease in the electrical conductivity, due to the GNP fragmentation. Instead, the thermal conductivity is enhanced due to the higher homogeneous distribution of GNPs into the epoxy matrix. Finally, the lower surface area of GNPs reduces the thermal and electrical conductivity due to a greater separation between nanosheets. Regarding the study of the attenuation of electromagnetic waves, it has been discovered that in the frequency range from 100 Hz to 20 MHz, this attenuation is independent of the direction of analysis, the type of graphene, the sonication time, and the state of dispersion of the nano-reinforcement in the matrix. Furthermore, it has also been observed that the conservation of the constant shielding values for the three types of GNPs are in a range of average frequencies between 0.3 and 3 MHz.