Analyzing Point Distributions in Voronoi Tessellations from Two Probability Sources $p$ and $\tilde{p}$

Question

Let's suppose I have a probability distribution $p$ and another distribution $\tilde{p}$. Suppose I sample $K$ points from the distribution $p$ which will be my centroids for my Voronoi tessellation. Now let's say I sample $N$ points from my other distribution. I want to know if there exists any result about the distribution of points in each tessellation cell (i.e., for example, whether they follow a uniform distribution, i.e., roughly the same number of points in each cell) and the relationship between $p$ and $ \tilde{p}$. Thank you very much.