Assume a society where all girls take their husbands surnames on marriage. It then follows that there will be an exponential decrease in the No. of surnames in that society, since some fathers will have only daughters. For example, if all families have just 2 children, about 25% will have 2 daughters, leading to a loss of 25% of the surnames available each generation. After 10 generations, only about 5.6% of the original number of surnames would remain. There are a lot of odd names in Dickens; I always thought he'd made them up, but perhaps they've died out.... Since we aren't all called Smith, and the phone book shows plenty of names, my model is obviously over-simplified, and there must be a source of new surnames coming into society - from where, and how?