This work deals with the stabilization of premixed turbulent swirling flames of methane/hydrogen/air combustible mixtures with different dilution rates of nitrogen and carbon dioxide. A central bluff body helps stabilizing the flames at low swirl numbers. The flame tip eventually impinges the combustor peripheral wall. The general objective is to gain understanding of the mechanisms governing the stabilization and the topology of these flames. It is found that the swirl number, the combustible mixture composition, the geometry of the combustor, and the thermal boundary conditions have a strong impact on the shape taken by these flames. The experimental setup used to characterize flames topologies is first described. Flames prone to topology...