Family name distributions: Master equation approach
  Although cumulative family name distributions in many countries exhibit power-law forms, there also exist counterexamples. The origin of different family name distributions across countries is discussed analytically in the framework of a population dynamics model. Combined with empirical observations made, it is suggested that those differences in distributions are closely related with the rate of appearance of new family names. 
Seung Ki Baek, Hoang Anh Tuan Kiet, and Beom Jun Kim