We use wave-optics simulations to investigate branch-point density (i.e., the number of branch points within the pupil-phase function) in terms of the grid sampling. The goal for these wave-optics simulations is to model plane-wave propagation through homogeneous turbulence, both with and without the effects of a finite inner scale modeled using a Hill spectrum. In practice, the grid sampling provides a gauge for the amount of branch-point resolution within the wave-optics simulations, whereas the Rytov number, Fried coherence diameter, and isoplanatic angle provide parameters to setup and explore the associated deep-turbulence conditions. Via Monte Carlo averaging, the results show that without the effects of a finite inner scale, the branch-point density grows without bound with adequate grid sampling. However, the results also show that as the inner-scale size increases, this unbounded growth (1) significantly decreases as the Rytov number, Fried coherence diameter, and isoplanatic angle increase in strength and (2) saturates with adequate grid sampling. These findings imply that future developments need to include the effects of a finite inner scale to accurately model the multifaceted nature of the branch-point problem in adaptive optics.