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Résumé : To self-renew, stem cells must precisely balance proliferation and differentiation. Typically, this is achieved under feedback from the niche; yet many stem cells also possess an intrinsic self-renewal program that allows them to do so autonomously, as required. However, because self-renewal implies a stable equilibrium - in which the expected stem cell number neither increases nor decreases over time - this seems to require fine-tuning to a critical point. Here, we show that this is not the case: self-renewal can, in principle, be easily achieved without the need for extrinsic instruction, feedback or finetuning, by a simple dimerization cycle that uses partitioning errors at cell division to reliably establish asymmetric divisions and perfectly balance symmetric divisions.