Map of percentage of people with European* ancestry, largely based in Ethnic self identification in censuses and in a broad ethnoreligious approach.
(English is not my  native language so forgive my mistakes)

The very concept of "European peoples" is contested. "Europe" itself is not a geographical accurate term, given the fact that the borders between Europe and (specially) Asia are historical, cultural and political more than physical. Read more here: https://en.wikipedia.org/wiki/Boundaries_between_continents#Europe_and_AsiaIn the latest version of this map I'm considering all ethnic groups with an European homeland since at least several centuries as "Europeans". So all North Caucasus peoples, Bosniaks, Albanians are considered Europeans.Turkey, Azerbaijan are non-europeans cultures (they are definitely not European descent).Datas about California, USA and Washington, USA were corrected because we must count all white population (white alone), not only non-hispanic white.Some groups in the Ural/Volga border as the Nenets and the Kalmyk peoples are not considered Europeans due to their strong historical ties to Siberia and Mongolia, but this is debatable.West Afroasian Christians as Egyptian Copts and Arab Christians are not considered European.Mixed race people: different criteria so explanations are given. Mixed race people are often counted separately in  many censuses and follow the one drop rule (one drop of non European blood means that people is out of the European ancestry group and into the Mixed ancestry or even African/Asian group). Whenever this is the case, I just follow the census country criterion. For example, the USA follow the one-drop rule, so African-Americans with 20% African ancestry and  80% European would count  as 0% European ancestry in this  map). Given the fact "Mestizo" and "Colored" are separate categories in many censuses (in Latin America or South Africa) from "White" or "European", I'm considering those 0% European ancestry despite the fact those people probably have European ancestry, because of lack of genetic data (the answer to questions like "are Mestizos 10% European or 90%?" is really hard to find in many countries, so I'm being conservative). Other issue can be found in how people identify themselves in Latin American and other mixed-race countries: a 80% Amerindian 20% European mixed race population self identified as "White", "Caucasoid" or "European" is counted as 100% European ancestry in this map. So numbers are sometimes inflated, and sometimes reduced to some point. Obviously no massive DNA analysis are performed in censuses so we rely on the information they gather based in self identification and this map has to be read in that way. Anyway, I'm not using the one-drop rule, but the genetic admixture rule, in some  cases when the census is not explicit about this and I have to take a decission  AND I happen to have genetic precise data: for example, mixed Asian-European groups in Russia (like Mari people) are counted as (for example) 30 to 70% European ancestry following genetic studies on Mongoloid admixture (which I managed to find) in every Eurasian ethnic group . Also check the sources for more information, a lot of data is gathered from the European Diaspora article so I'm not deeply following every link, but just assuming that data is acceptable and accurate in a broad sense. Ask the original editors of this article for further information. Anyway, numbers and percentages probably  don't change so much after all these calculus, so the map is correct in general (maybe take a +-10% error in Eurasia and +-20/30% in Latin America, where ancestries are much more mixed). In Chile, lack of self identification ancestry in censuses led me to search genetic data as well.This is NOT a map of the White race, just an "European ancestry" map. Thats the reason North African, Middle Eastern and Indo-Iranian peoples majority territories are not shaded. Anyway, some countries don't specify the origin of "White people" in their censuses so I'm taking "Caucasian" and "White" self identified people in censuses mostly in countries in the Americas as having "European ancestry", so Lebanese ancestry people in Colombia or Morocco ancestry people in the USA are counted as "European ancestry" peoples in this map because of lack of data. Despite of that, numbers and percentages wouldn't be so different considering those details and I encourage everyone who is reading this to do the math and realize these facts.To sum it up all, generally conservative criteria are taken: the geographical criterion (Middle Eastern Christians and Indo-Iranians are not considered European because their historical roots are in zones of the Asian continent) or the census one-drop-rule criterion (Mixed race peoples with lack of genetic data are not considered European). With other and broader criteria, the map would be completely different and it could be redrawn.Kurds, Iranians and Kazakhs are not considered here Europeans as ethnic groups that are related or belong to Asian territories.Source base map: File:Blank_Map_World_Secondary_Political_Divisions.svg
My original sources were a mixture between data in the article ( https://en.wikipedia.org/wiki/European_diaspora ) where the map is, and in countries where the information is detailed enough are taking numbers from censuses from the Russian Wikipedia for all the provinces, oblasts, autonomous regions, etc(see below), censuses from the USA 2010 (numbers listed in https://www.census.gov\/prod/cen2010/briefs/c2010br-05.pdf https://en.wikipedia.org/wiki/White_American ), Australian 2011 census http://www.abs.gov.au/census , and Canada (numbers listed in https://en.wikipedia.org/wiki/Demographics_of_Canada ), and taking into account the number of non-European migrants in the countries of the EU https://en.wikipedia.org/wiki/Immigration_to_Europe .
Kazakhstan: Each province was searched, I went to the russian article where ethnic compositions are given (in Russian). For example, the Akmola region: https://en.wikipedia.org/wiki/Regions_of_Kazakhstan https://ru.wikipedia.org/wiki/%D0%90%D0%BA%D0%BC%D0%BE%D0%BB%D0%B8%D0%BD%D1%81%D0%BA%D0%B0%D1%8F_%D0%BE%D0%B1%D0%BB%D0%B0%D1%81%D1%82%D1%8C Same with the rest (take all the provinces, look for them in the Russian wikipedia, etc): https://ru.wikipedia.org/wiki/%D0%90%D0%BA%D1%82%D1%8E%D0%B1%D0%B8%D0%BD%D1%81%D0%BA%D0%B0%D1%8F_%D0%BE%D0%B1%D0%BB%D0%B0%D1%81%D1%82%D1%8C https://ru.wikipedia.org/wiki/%D0%90%D0%BB%D0%BC%D0%B0%D1%82%D0%B8%D0%BD%D1%81%D0%BA%D0%B0%D1%8F_%D0%BE%D0%B1%D0%BB%D0%B0%D1%81%D1%82%D1%8C I continued with the rest. Russia: http://pop-stat.mashke.org/russia-ethnic2002.htm  Brazil: File:People_of_European_Ancestry_in_Brazil.png
Bosnia-Herzegovina:  https://en.wikipedia.org/wiki/Religion_in_Bosnia_and_Herzegovina
Kosovo: https://en.wikipedia.org/wiki/Demographics_of_Kosovo#Religion
Albania:

https://en.wikipedia.org/wiki/Religion_in_Albania
Own work
Nagihuin