Não é dependia de qualquer critério, ele depende principalmente gene Um assistente tem que nasce com o gene mágico independentemente de seus pais.
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Those born to Muggle families but who are skilled with and have the magic gene are referred to as Muggle-borns. A child born with magic to two Muggle parents is considered a Muggle-born.
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Muggle-born is the term given to a witch or wizard who is born to two non-magical parents. Their magical abilities do not seem to be at all affected by their Muggle parentage. In fact, many Muggle-borns have been among the most talented witches and wizards of their time, such as Lily Evans and Hermione Granger.
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Muggle-borns will have a witch or wizard somewhere on their family tree, in some cases many, many generations back. The gene resurfaces in some unexpected places.
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Muggle-borns are descendants to Squibs. You can consider magic being some form of genetic marker that can go dormant and resurface years or centuries later even.