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Living cells use phase separation and concentration gradients to organize chemical compartments in space. Here, we present a theoretical study of droplet dynamics in gradient systems. We derive the corresponding growth law of droplets and find that droplets exhibit a drift velocity and position dependent growth. As a consequence, the dissolution boundary moves through the system, thereby segregating droplets to one end. We show that for steep enough gradients, the ripening leads to a transient arrest of droplet growth that is induced by a narrowing of the droplet size distribution.