This paper investigates proactive data dissemination and storage schemes for Wireless Sensor Networks (WSNs) with mobile sinks. The focus is on schemes that do not impose any restrictions on the sink's mobility pattern. The goal is to enable the sink to collect a representative view of the network's sensed data by visiting any set of x out of n nodes, where x << n. The question is how to obtain this while maintaining a good trade--off between the communication overhead of the scheme, the storage space requirements on the nodes, and the ratio between the number of visited nodes x and the representativeness of the gathered data. To answer this question, we propose DEEP (Density--based proactivE data dissEmination Protocol), which combines a probabilistic flooding with a probabilistic storing scheme. The DEEP protocol is formally analyzed and its performance is studied under simulations using different network densities and compared with a scheme based on random walks, called RaWMS.