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High-altitude balloons are a promising technology for providing high-speed wireless Internet to the entire Earth. These balloons float passively on wind currents in the stratosphere and connect to nearby Internet users on Earth. To connect to everyone on Earth, a fleet of several thousands balloons must be arranged in an evenly spread-out formation, so that every user is close to at least one balloon. Since the balloons naturally move with the wind, an important problem is to control the formation of the fleet of balloons. In this paper, we show that distributed extremum-seeking control (ESC) can be used to control the balloon formation. This approach is based on the minimization of a cost function and does not require a model of wind currents or Internet users. We provide several cost functions, which can be used by the ESC and are based on the distance between balloons, Voronoi partitions, a variant of Lloyd's algorithm, Internet bandwidth, and the number of Internet users. As the control architecture is fully distributed, the computational burden is shared between all the balloons, and the algorithm can be scaled to an arbitrarily large network of balloons. Several simulations involving 1200 balloons are used to verify the effectiveness of this approach. The simulations use realistic nonlinear wind models, which are obtained by interpolating gridded weather data obtained from the National Oceanic and Atmospheric Administration.