We describe a framework for better understanding scheduling policies for fine-grained parallel computations and their effect on space usage. We define a profiling semantics that can be used to determine the asymptotic space taken by any schedule. A nondeterministic parallel transition semantics is used to describe all possible parallel executions. Refinements of that semantics can be used to model the behavior of particular schedulers. We use the framework to show that different schedules can lead to asymptotic differences in space usage.