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Wiktionary
birth tourism

n. (context idiomatic English) Travel from one country to another for the purpose of giving birth in the second country, thereby endowing the newborn child with citizenship of the second country.

Wikipedia
Birth tourism

Birth tourism is travel to another country for the purpose of giving birth in that country. "Anchor baby" is another related term which can have negative connotations. Reasons for the practice include access to the destination country's healthcare system, circumvention of China's one-child policy and in countries that recognize jus soli birthright citizenship for the child. The United States and Canada are popular destinations for birth tourism. Another target of birth tourism is Hong Kong, where the right of abode is awarded to Chinese citizens at birth instead of citizenship.

To discourage birth tourism, Australia, France, Germany, Ireland, New Zealand, South Africa, and the United Kingdom have modified their citizenship laws at different times, granting citizenship by birth only if at least one parent is a citizen of the country or a legal permanent resident who has lived in the country for several years. Germany has never granted unconditional birthright citizenship, but has traditionally used jus sanguinis, so, by giving up the requirement of at least one citizen parent, Germany has softened rather than tightened its citizenship laws; however, unlike their children born and grown up in Germany, non-EU- and non-Swiss-citizen parents born and grown up abroad usually cannot have dual citizenship themselves. See also German nationality law.

No European country presently grants unconditional birthright citizenship; however, most American countries, e.g. the United States, Canada, Mexico, Argentina, and Brazil do so. In Africa, Lesotho and Tanzania grant unconditional birthright citizenship, and so do in the Asian-Pacific region Fiji, Pakistan, and Tuvalu,