The catalytic decomposition of methane (CDM) is a H-2 production process in which the CO2 emission of conventional processes is avoided and from which carbon nanofilaments can be obtained as a high added value byproduct. In this work, we present a thermogravimetry-based screening of catalysts according to their carbon production in the CDM reaction. Catalysts studied were based on Ni as active phase, using two textural promoters (Al2O3 or MgO) and Cu as dopant element in different proportions: 2.5, 5.0, 7.5 and 10 mol %. Cu doping resulted in an increase in both the maximum temperature of activity (> 100 degrees C) and the carbon formation rate, which were maximum for a Cu content of 7.5 mol %, regardless of the textural promoter used. The formation of a solid solution of NixCu(1-x), with lattice constants and particle size distribution highly dependent on the Cu content, led to the formation of fishbone carbon nanofibers with different morphological features, such as the a angle between the graphene stacks and the growth axis of the nanofilament, the diameter, the length and the formation or not of an inner hollow.