Message Broadcasting in Opportunistic Networks is based on the opportunity of establishing contacts among mobiles nodes for message exchange. Nevertheless, as the amount of information transmitted in a contact is limited by the transmission speed and the contact duration, large messages are less likely to be exchanged, and thus their diffusion is severely limited. Furthermore, these failed transmissions can also lead to an important waste of network resources, since the message transmission is aborted when the contact ends and the message needs to be transmitted again in the next contact. Therefore, in this paper we study the impact that contact duration has on the broadcast of messages, showing that splitting a large message into smaller parts can improve its diffusion. Based on this idea, we propose an extension of the epidemic protocol called Xpread. The efficiency of this protocol mainly depends on how the original message is partitioned. Thus, in order to evaluate the impact and the efficiency of the partition scheme, we have developed an analytical model based on Population Processes, showing that a fixed size partition is the best option, while also providing a simple expression to obtain the optimal size. The Xpread has been evaluated exhaustively using four different mobiles traces, comprising both pedestrian and vehicular scenarios. The results show that the diffusion of large messages is improved up to four times with a slight reduction in the delivery time and overhead, minimising also message forwarding failures.