I have previously posted on the heavy-tailed or power law nature of income distributions where income and number of people with that income has a power relationship. (See Who cares about the average income!)
To get a feel for how much of Nature can be described by a power law and what could be behind this, here is a good book to start with: How Nature Works by Per Bak. Per Bak (now no more) was a physicist who developed a model that he called ‘self-organized criticality’ that produces power law outcomes. However, it is not the only model of dynamical systems that produces power laws. Consequently he did get quite a bit of criticism for stretching to claim that this (his model) is how nature works. Nonetheless it is an interesting read.
As a general principle though, models of systems that produce power laws (like the one developed by Per Bak) are ones that are dynamic or in motion, and by their very nature are able to explain the coexistence of the few very large events (the accumulation of billions among a small number of individuals) and the large number of very small events (a huge number of people who have not acquired much money at all). This is a fundamental shift in thinking relative to the prevailing notion that the existence of billionaires (or rare events) is ‘anomalous’. Indeed billionaires appear to be a natural outcome of a dynamical system of money flow.