Juana Miró was Moixina's last wife. Like Martí, Miró is widespread across the Catalan-speaking world; the painter Joan Miró, for instance, was from Barcelona and unrelated to these families.
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Start with what your family has: baptism, marriage and death records of your parents, grandparents and great-grandparents, including their second surnames (Spanish naming uses both parents' surnames).
With those details you can search the parish registers of Palma, above all Santa Eulàlia, the parish of the old Jewish quarter, and the Diocesan Archive of Majorca.
The trial records of the Majorcan Inquisition are held in Spain's National Historical Archive, and many can be viewed online through the PARES portal.
Carrying the surname does not prove descent; the chain of documents does. Tell us your story and we will point you in the right direction.