We analyze digital markets where a monopolist platform uses data to match multiproduct sellers with heterogeneous consumers who can purchase both on and o§ the platform. The platform sells targeted ads to sellers that recommend their products to consumers and reveals information to consumers about their values. The revenueoptimal mechanism is a managed advertising campaign that matches products and preferences e¢ ciently. In equilibrium, sellers o§er higher qualities at lower unit prices on than o§ the platform. Privacy-respecting data-governance rules such as organic search results or federated learning can lead to welfare gains for consumers.