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The main contribution of this work is to propose OSCAR - an opportunistic call admission protocol that provides a simple and robust solution to call admission and handoff management in LEO satellite networks. One of the features that sets OSCAR apart from existing protocols is that it avoids the overhead of reserving resources for users in a series of spotbeams along predicted user trajectories. Instead, OSCAR relies on a novel opportunistic bandwidth allocation mechanism that is very simple and efficient and does not involve maintaining complicated data structures or making expensive reservations. Extensive simulation results have shown that OSCAR achieves results comparable to those of Q-Win: it features very low call dropping probability, thus providing for reliable handoff of on-going calls, low call blocking probability for new call requests, and high bandwidth utilization.