The legal rehabilitation of a nobility title in Spain requires the following:

1) You must present all documentation of baptismal and/or birth certificates, as well as marriages of your ancestors until you join the first bearer of the title.

2) All these certifications must be certified by the consuls of Spain in their function as notaries, who must travel to the parish archives where the baptismal and marriage books prior to the Civil Registry are. In addition, the Civil Registry items must bear all the Apostille of the Hague Convention.

3) You must also provide the testamentary of all your ancestors all the way up to the first bearers: wills or deeds of partition of property, from the first bearer to you. With the Apostille of The Hague, naturally.

4) You must claim and prove merits, because just as the succession is automatic, the rehabilitation is also subject to grace. That is, that the King can grant it or not, taking in account the reports of this Council of the Diputación de la Grandeza and the Council of nobility titles of the Ministry of Justice.

5) Last but not least, the decision of the King is by grace, so even in the case that someone gathers all the documentation and has sufficient merits, it could happen that the King decides to not grant the rehabilitation. The King has the last word.

In the event that the rehabilitation was granted, you would have to pay the tax, the amount for this year 2019 is 4783 euros.

That is how it must be done and you can read more about it HERE.

How can you check if a nobility title is real in Spain?

https://www.diputaciondelagrandeza.es/guiadetitulo/

Titles are displayed in the Official Website of the Diputación de la Grandeza.

Los diviseros se inscriben en 7 divisas. Para su proceso de "asentamiento", un nuevo divisero, debe acreditar, mediante pruebas documentales fehacientes, la descendencia de diviseros previamente inscritos en el Solar y su registro genealógico, siendo este proceso supervisado y verificado por la **Junta de Probanza**, que emitirá un juicio y procederá o no a su inscripción en los libros de asentamientos que se conservan desde el siglo XVI hasta nuestros días. De acuerdo con la Real Cédula de Enrique IV de Castilla, se consideran válidas tanto las líneas de varón como de mujer, lo que ha propiciado la expansión de los descendientes por todo el mundo. https://es.wikipedia.org/wiki/Señorío_del_Solar_de_Tejada

http://lamesadelosnotables.blogspot.com/2018/02/
Integrada por grandes de España, títulos del reino e hidalgos se gobierna mediante tres órganos directivos: el Capitulo General, el Consejo de Nobles y la Junta de Probanza.

https://en.wikipedia.org/wiki/Spanish_nobility
In Spain today, the possession of a title of nobility does not imply any legal or fiscal privilege; On the contrary, the possession of titles of nobility is subject to the payment of a normal level of taxation. It is a distinction of merely honorary and symbolic character, accompanied by the treatment of the most excellent lord for those titles that possess the dignity of grandees of Spain and of illustrious lords for others. The last privilege, suppressed in 1984, was the right to a diplomatic passport by the grandees of Spain (Grandes de España). This privilege disappeared by Royal Decree 1023/1984. The titles without the rank of grandee of Spain never enjoyed this privilege.

With the establishment of the Second Spanish Republic in 1931, the use of noble titles was abolished by way of Decree of 1 June 1931,[4] ratified by Law of 30 December of the same year.[5] In 1948, legal recognition of the usage of noble titles was provided for by Law of 4 May 1948 restoring the rules as they were before 14 April 1931.[6]

At present, titles of nobility find their legal basis in article 62, section f, of the 1978 constitution, which grants the prerogative of the king to grant honors and distinctions in accordance with the laws.

Spanish legislation recognizes titles of nobility and protects their legal owners against third parties. The Spanish nobility titles are in no case susceptible of purchase or sale, since their succession is strictly reserved for blood relatives of better right of the first holder of the title. The successions are processed by the Ministry of Justice and their use is subject to their respective tax.

https://read.dukeupress.edu/ethnohistory/article-abstract/64...
https://read.dukeupress.edu/ethnohistory/search-results?page...
... present-day Puerto Rico. The 1532 probanza of Juan González is privileged as a text through which crucial information concerning the Spanish colonization of San Juan and its original inhabitants could be obtained. The article thus contextualizes the probanza as part of a genre of colonial writing within...

https://publishing.cdlib.org/ucpressebooks/view?docId=ft1q2n...
probanza: proof (evidence or testimony relating to a person's antecedents, activities, etc.)

(PDF) Testimonies of the Spanish-Indigenous Conquest ...www.researchgate.net › publication › 298565936_Testim...
Testimonies of the Spanish-Indigenous Conquest: Hernando Cortes, Tepexic, and ... discerned from the Tepexic nobility's testimony in the probanza, the alliance ...

Ethnological Hermeneutics for an Early Colonial Encounter on ...read.dukeupress.edu › ethnohistory › article-standard › Et...
Apr 1, 2017 — probanza, Juan González, San Juan, Puerto Rico, Taíno, Caribs ... as a deserter with a testimonial narrative in which he was portrayed as a highly ... tells us that González actually came from an aristocratic lineage (AGI, fol.


Cacique-hidalgos (Chapter 5) - Indigenous Elites and Creole ...www.cambridge.org › core › caciquehidalgos › core-reader
In some ways, cacique testimonies in the mature colony remained essentially ... His probanza (legal proof of merits) boasted of noble Iberian roots, and began ...

In fact, many links just leave the term "Probanza" which may be one way to deal with it along with an explanation in brackets, such as "legal proof of merits", or "proof (evidence or testimony relating to a person's antecedents, activities, etc.)".

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Note added at 22 hrs (2021-01-08 14:04:03 GMT)
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David, you don't have to go thru Support. I will enter the phrase as an answer. This was a reference, so that is why you do not see an option to select an answer.