Let's say that I have a rectangular two-dimensional surface of bounded dimensions, $[0,A]$ and $[0,B]$:

Under "no overlap" constraints, I sequentially deposit circles of radii $r_c$ on this surface, where the center-point of each circle is allowed real number coordinates and is chosen with uniform probability. To address concerns related to edge conditions, only the center-point of each surface needs to be on the bounded plane. If a set of random coordinates imply an overlap with one or more previously deposited circles, a new set of random coordinates is chosen. Under no conditions may any of the previously placed circles be rearranged.

Under these conditions, approximately how many circles, $N$, should I be able to pack onto the plane? What average-case maximum packing density is achievable?