The rank-size distribution might be worth looking into. The basic principle is that a city's population size rank is roughly the divisor of the largest city's population. So the 2nd largest city is generally half the size of the largest, the third largest is a third of the size, etc.
But an often overlooked factor is the history of industrialization. The rank-size distribution is something like an equilibrium that takes time to manifest. Industrialization can be one of the most drastic social changes a society will face and in general, the later you are to the party, the faster you will industrialize. England took a century, France and Germany took 50 years, Kenya took a decade or less. (these times are probably wrong, but you get the idea) Industrialization is generally focused on a particular geographic area. A good port, a good source of coal or iron ore, something makes a particular place a good place to invest. And investment breeds investment. This leads to a particular city becoming far more attractive than others and can lead to urban primacy where the population of one city vastly surpasses any others.
Today, this is common in South America, Africa and southeast Asia because of the rapid pace of industrialization. Primate cities generally have a hard time providing services to so many people and can probably be assumed to be worse places to live. However, it should be noted that these cities often have so many people because they have much more opportunity than surrounding cities. Locally, they are attractive places, but compared to other cities of their size, they're generally worse off. Rank-size distributions are generally indicative of a stable, long-term economic situation and primate cities are often indications of fairly recent upheaval.
As far as how big that largest city is, that should have something to do with communication and transportation technology. For example, Venice today literally cannot grow because there can be no trucks and all deliveries to keep stores stocked are done so by foot. Of course, there's other demographic issues to Venice, but the transportation system is a hard limit on that city's growth. Better transportation and communication enables bigger cities, both in population and footprint. Might be worth keeping in mind density is a controlled factor that a state can regulate. Crowding is a psychological construct that can result from poorly managed density.