We study competition in persuasion with multiple senders in linear Bayesian persuasion games, where each sender's payoff depend only on the receiver's posterior expectation about a uni-dimensional state. Our main result provides a partial geometric characterization for equilibrium outcomes that are minimally informative. Building on this, we establish the sufficient and necessary condition for senders' competition to induce full information disclosure in all equilibria. We apply this condition to a game in which multiple senders compete in persuading a privately informed receiver to take a binary action. There, we show that a strong conflict of interests between senders is neither sufficient nor necessary to robustly -- i.e., independently of the distributions of the state and the receiver's private type -- induce full disclosure as the unique equilibrium outcome. We provide economically meaningful sufficient conditions for such robust full disclosure. Finally, we derive sufficient conditions that ensure a receiver to be strictly better off by exploiting senders' competition instead of consulting any single sender.