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Opportunistic networks are created dynamically by exploiting contacts between pairs of mobile devices that come within communication range. While forwarding in opportunistic networking has been explored, investigations into asynchronous service provisioning on top of opportunistic networks are unique contributions of this paper. Mobile devices are typically heterogeneous, possess disparate physical resources, and can provide a variety of services. During opportunistic contacts, the pairing peers can cooperatively provide (avail of) their (other peer's) services. This service provisioning paradigm is a key feature of the emerging opportunistic computing paradigm. We develop an analytical model to study the behaviors of service seeking nodes (seekers) and service providing nodes (providers) that spawn and execute service requests, respectively. The model considers the case in which seekers can spawn parallel executions on multiple providers for any given request, and determines: 1) the delays at different stages of service provisioning; and 2) the optimal number of parallel executions that minimizes the expected execution time. The analytical model is validated through simulations, and exploited to investigate the performance of service provisioning over a wide range of parameters.