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                <term xml:lang="en">Many-to-one formula</term>
                <term xml:lang="en">Size biased reproduction distribution</term>
                <term xml:lang="en">Eigenproblem</term>
                <term xml:lang="en">Deterministic macroscopic approximation</term>
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              <p>We consider a particle system in continuous time, discrete population, with spatial motion and nonlocal branching. The offspring's weights and their number may depend on the mother's weight. Our setting captures, for instance, the processes indexed by a Galton-Watson tree. Using a size-biased auxiliary process for the empirical measure, we determine this asymptotic behaviour. We also obtain a large population approximation as weak solution of a growth-fragmentation equation. Several examples illustrate our results.</p>
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