We show that donors that maximize relative aid impact spread their budgets across many recipient countries in a unique Nash equilibrium. This aid fragmentation result is robust to the introduction of fixed costs, even if they are improbably large. In equilibrium, smaller donors have less fragmented aid, and behave better from an efficiency viewpoint. We present evidence that our theoretical results are in line with cross-country correlations. Our analysis has important policy implications: First, short of ending donors' maximization of relative aid impact, agreements to better coordinate aid allocations are not implementable. Second, since policies to increase donor competition in terms of aid effectiveness risk reinforcing relativeness, they may well backfire, as any such reinforcement increases aid fragmentation.