The Kolpak rule relates to a case brought by Slovenian handball player Maros Kolpak. He played league handball in Germany and complained to the EU court of human rights that he was being discriminated against by a rule that stated clubs in the league couldn't field more than three players from outside the EU. He argued successfully that, as Slovenia have special trade arrangements with the EU, he should be afforded the same rights of movement and freedom of employment as an EU citizen.
How this applies to cricket is that the Caribbean nations and South Africa come under the same trade arrangements with the EU as does Slovenia, so you end up with a lot of South Africans playing county cricket in England who are not counted as overseas players (counties are only allowed one overseas player as per league rules - two for 2010's Twenty20 competition).
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