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We encode the genealogy of a continuous-state branching process associatedwith a branching mechanism $\Psi$ - or $\Psi$-CSBP in short - using astochastic flow of partitions. This encoding holds for all branching mechanismsand appears as a very tractable object to deal with asymptotic behaviours andconvergences. In particular we study the so-called Eve property - the existenceof an ancestor from which the entire population descends asymptotically - andgive a necessary and sufficient condition on the $\Psi$-CSBP for this propertyto hold. Finally, we show that the flow of partitions unifies the lookdownrepresentation and the flow of subordinators when the Eve property holds.

Genealogy of flows of continuous-state branching processes via flows of partitions and the Eve property