We analyze the evolution of cumulative national shares of Nobel Prizes since 1901, properly taking into account that most prizes were divided among several laureates. We rank by citizenship at the moment of the award, and by country of birth. Surprisingly, graphs of this type have not been published before, even though they powerfully illustrate the century's migration patterns (brain drains and gains) in the sciences and other fields. The Nobel Foundation does not treat all Nobel Laureates equally. While some get a full prize for their achievements, most get only 1/2, 1/3, or 1/4. For example, some Nobel Prizes are divided among three laureates such that one of them gets 1/2, and the others 1/4 each. Our data gathered from the Nobel Foundation web site nobelprize.org (retrieved in March 2010) takes this into account. For the most successful nations of the 20th century, our figures show the temporal evolution from 1901 to 2000 (and up to 2009) of national Nobel Prize shares, by c...