While Amazonian forests are extraordinarily diverse, the abundance of trees is skewed strongly towards relatively few 'hyperdominant' species. In addition to their diversity, Amazonian trees are a key component of the global carbon cycle, assimilating and storing more carbon than any other ecosystem on Earth. Here we ask, using a unique data set of 530 forest plots, if the functions of storing and producing woody carbon are concentrated in a small number of tree species, whether the most abundant species also dominate carbon cycling, and whether dominant species are characterized by specific functional traits. We find that dominance of forest function is even more concentrated in a few species than is dominance of tree abundance, with only ≈1% of Amazon tree species responsible for 50% of carbon storage and productivity. Although those species that contribute most to biomass and productivity are often abundant, species maximum size is also influential, while the identity and ranking of dominant species varies by function and by region.