Our study employs the distribution dynamics approach to uncover transition probabilities and the long-term evolution of relative per capita carbon emissions (REPC) and relative carbon intensity (REPGDP) across 204 countries. We split the period of analysis into pre-crisis (2000-2007), and post-crisis (2007-2016) and divided countries into four income groups. The results indicate the emergence of new convergence clubs post-crisis in both REPC and REPGDP. On the one hand, the majority (many) of the low- (high) income countries congregate to extremely low (above the global average) REPC levels in the long run. On the other hand, most of the upper-medium- (high) income economies cluster around REPGDP levels far above (below) the global average. Finally, using mobility probability plots, we identify above-average carbon emitters with the highest probabilities of diverging further above the global average in the coming years. The study delivers nascent evidence supporting the usefulness of the MPP display tool in clarifying the positions and responsibilities of specific countries in future agreements on climate change. The results support the argument for using both measures of carbon emissions as a suite of future multilateral climate negotiations and policies.