Message delivery in opportunistic networks is substantially affected by the way nodes move. Given that messages are handed over from node to node upon encounter, the intermeeting time, i.e., the time between two consecutive con- tacts between the same pair of nodes, plays a fundamental role in the overall delay of messages. A desirable property of message delay is that its expectation is finite, so that the performance of the system can be predicted. Unfortunately, when intermeeting times feature a Pareto distribution, this property does not always hold. In this paper, assuming het- erogeneous mobility and Pareto intermeeting times, we pro- vide a detailed study of the conditions for the expectation of message delay to converge when social-oblivious forwarding schemes are used. More specifically, we consider different classes of social-oblivious schemes, based on the number of hops allowed, the number of copies generated, and whether the source and relay nodes keep track of the evolution of the forwarding process or not. Our main finding is that, as long as the convergence of the expected delay is concerned, al- lowing more than two hops does not provide any advantage. At the same time, we show that using a multi-copy scheme can, in some cases, improve the convergence of the expected delay. Copyright 2012 ACM.