We encode the genealogy of a continuous-state branching process associated with a branching mechanism $𝛹$ – or $𝛹\text{-CSBP}$ in short – using a stochastic flow of partitions. This encoding holds for all branching mechanisms and appears as a very tractable object to deal with asymptotic behaviours and convergences. In particular we study the so-called Eve property – the existence of an ancestor from which the entire population descends asymptotically – and give a necessary and sufficient condition on the $𝛹\text{-CSBP}$ for...