Part 1 - France
Many of us dream of the day when the GRO indexes are computerised. We must look with envy to France where this has been done in part - birth registrations - for two separate periods, 1891-1915 and 1916-1940.
These two databases of the surnames registered at birth reveal:
1891-1915: Number of Names
There are 489,000 births indexed in this database, [for] 36% of which the surnames only occur once.
1916-1940: Number of Names
There were 605,438 births registered in this second period, of which 172,916 surnames or almost 30% only occur once.
Total size of the surname stock
The databases record only births. The size of the surname stock must be of a different order [to the number of births]. This is extrapolated from the databases as:
Average number of surnames per département
Highest-ranking French Surnames
But French common surnames were not predominantly diffuse like English ones
Regional high-ranking surnames pre-World War 1
Nationally-distributed high-ranking surnames pre-World War 1
(Source: French data translated and condensed from Pierre Darlu, Anna Degioanni and Jacques Ruffie Quelques statistiques sur la distribution des Patronymes en France, which appeared in Population Vol 52 Part 3, 1997.)
Part 2- Current Comparisons
There are 85,000 different surnames in Denmark, but 64% of the population is included in the 50 most common. This figure is derived from the computerised Danish Central Civil Register.
Estonians acquired family names in large numbers in the 1820s-1830s. A database of Estonian family names, Corpus Nominum Gentilium Estonicorum, is to be released on the web. This database will "consist of two parts: the database of original homes of family names (73,928 entries) and the database of changed names (78,777 entries). The database is linked with a digital map projection that enables to search data about the territorial distribution of a name... The variety of names among such a small nation was exceptionally wide: 41,000 different names (in a number of cases it was also caused by a (purposely) different spelling), among them ca 3/4 unique, i.e., they occurred only in one community, in one family." Source: Icos 2002 meeting abstracts.
Central Finnish surname registry
The Database of surnames in the Netherlands was launched in January 2000 by the Meertens Instituut in Amsterdam. Intended to include articles about a name, an interpretation of the origins, early attestations, genealogical references, a list of variations, an overview of the frequency and geographical distribution, etcetera.
In a telephone directory analysis, 50% of the country’s surnames were only listed once.
Surnames have a very long history in China, but there are only 3,100 surnames in current use compared with nearly 12,000 in the past.
Until a few months ago  it was illegal for people of the same surname in South Korea to marry each other - and the majority of the population shared just 5 common surnames.
Originally a poster presentation for a Society of Genealogists One-Name Day, August 1999, prepared by Philip Dance