Graphene-based electrodes are very promising for molecular electronics and spintronics. Here we report a systematic characterization of the electroburning (EB) process, leading to the formation of nanometer-spaced gaps, on different types of few-layer graphene (namely mechanically exfoliated graphene on SiO2, graphene epitaxially grown on the C-face of SiC and turbostratic graphene discs deposited on SiO2) under air and vacuum conditions. The EB process is found to depend on both the graphene type and on the ambient conditions. For the mechanically exfoliated graphene, performing EB under vacuum leads to a higher yield of nanometer-gap formation than working in air. Conversely, for graphene on SiC the EB process is not successful under vacuum. Finally, the EB is possible with turbostratic graphene discs only after the creation of a constriction in the sample using lithographic patterning.