They don't. His family's monarchy was abolished long ago (1889). Thus he was born a common citizen just like everyone else in Brazil. He is no more legally a Brazilian prince than you or I.
And that's actually one of my pet peeves. Folks like him love to prance around with fancy royal titles and their fancy coats of arms. It's all baloney.
Signed,
Leaning Right
His Imperial and Royal Highness, The Prince Imperial of His Own Living Room
bump