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We study the local limit in distribution of Bienaym{\'e}-Galton-Watson treesconditioned on having large sub-populations. Assuming a generic and aperiodiccondition on the offspring distribution, we prove the existence of a limitgiven by a Kesten's tree associated with a certain critical offspringdistribution.

Conditioning Bienaym{\'e}-Galton-Watson trees to have large sub-populations