With the ever-growing number of cores per node, it is critical for runtime systems and applications to adapt the task granularity to scale on recent architectures. Among applications, sparse direct solvers are a time-consuming step and the task granularity is rarely adapted to large many-core systems. In this paper, we investigate the use of runtime systems to automatically partition tasks in order to achieve more parallelism and refine the task granularity. Experiments are conducted on the new version of the PaStiX solver, which has been completely rewritten to better integrate modern task-based runtime systems. The results demonstrate the increase in scalability achieved by the solver thanks to the adaptive task granularity provided by the StarPU runtime system.