A very nice piece on Zipf's Law in Brazil and in the US. Unfortunately there is a problem: the quality of the data on urbanization in Brazil. José Eli da Veiga has stressed how unreliable and insane are the 1938 official criteria on definition of urban areas in Brazil. Official data on urban population in Brazil is hugely overestimated and weirdly related to the number of municipalities created. Therefore, historical trends on urbanization in Brazil are unreliable and international comparisons should be avoided.
Recently, Embrapa used satellite images to identify urban areas and this is the best data that you can get. (The main limitation, obviously, is that there is no historical data)