The Fischer‐Tropsch reaction transforms syngas into high added value products, among which liquid fuels. Numerous parameters determine catalytic activity and selectivity towards the most desired hydrocarbons. The performances of cobalt‐based catalysts used in the reaction are known to depend critically on Co particle size and crystallographic phase. Here, we present a comparative study of Co‐based catalysts supported on three carbon supports: multi‐wall carbon nanotubes, carbon nanofibers and a fibrous material. Our results show that, while the selectivity towards C5+ follows the expected tendency with respect to Co particle size, this is not the case for the TOF. These results can be rationalized considering that the amount of H 2 uptake on each catalyst increases with oxygen and defect concentration on the support. The catalyst, on the support presenting many edges and oxygen surface groups, necessary for H 2 spillover, presents the highest activity. Furthermore, the hydrogen spillover contributes to the enhancement of olefin hydrogenation and methane production.