This may be old hat, but I had an interesting thought about the interplay between the concentration of wealth and fertility. It's well-known that as people get richer they tend to have fewer children, and to have them later in life. The natural result of this correlation is that over generations, wealthy families will dilute their resources much more slowly than average and poor families.
(Of course, many poor parents leave nothing to any of their children, but ignore the technicalities for the moment. There is probably a threshold level of wealth that must be met for children to receive anything from their parents, and the existence of such a threshold would further heighten the concentration of wealth effect.)
For example, consider two families, A and B, with equal wealth but differing fertility. Family A has 2 children every 33 years, and family B has 3 children every 25 years. After 100 years, the latest generation of family A will have 8 members (2*2*2), and the latest generation of family B will have 81 members (3*3*3*3). The wealth of the progenetors of family A will be far less diluted than the wealth of the progenetors of family B.
After 100 years, the aggregate wealth of family B may be greater than that of family A, simply due to its greater number of productive members. However, assuming that any member of either family is able to generate an equal amount of wealth on their own through working, the difference in wealth between any two individuals will be attributable to what they inherited from their ancestors. The concentration of wealth for family A will certainly be greater, and each individual member of A will be wealthier than each individual member of B.
Additionally, the members of these families will probably not care about their family's aggregate wealth, especially in the case of family B where the 81 great-great-grandchildren are unlikely to even know each other, much less be willing and able to wield their combined wealth toward any profitable end.
Aside from every other social and economic factor that encourages the concentration of capital, it appears that simple arithmetic creates a positively reinforced cycle that leads to the concentration of wealth. Even assuming equal-wealth starting conditions, differences in fertility will lead to differences in wealth, over time.