Gaudi, very very rare, would seem typical of Turin, of Castellamonte and Caselle Torinese, Gaudia is unique, Gaudielli is unique and should be a transcription error by Gaudiello, who is specifically from Campania, Neapolitan and Salerno in particular, Gaudini , very very rare, it is of central Italy, of Rome in particular, Gaudino has stocks in Lazio in Rome, and in the latinense in Gaeta and Latina, an important nucleus in Campania in the Neapolitan to Pozzuoli, Naples, Torredel Greco, Herculaneum, Portici, Frattaminore, Frattamaggiore, San Giorgio a Cremano and Casoria, in the Caserta area of Orta di Atella and Mondragone, and in the Salerno area at Pontecagnano Faiano and Nocera Inferiore, Gaudio is very widespread in Rome, Campania in the Caserta, Naples and Salerno areas, in the Bari area and above all in the Cosenza area, Cosenza and Mendicino, but with significant presences also to Longobardi, Dipignano, Fiumefreddo Bruzio, Rende, Castrolibero and Trebisacce, they should all derive, directly body or hypocoristic, from the late Latin name Gaudius, Gaudia (full of graces and goodness), of which we have an example in this writing of the second half of the 1500s: "... Antrorsum ante comites sederunt iustitiarii duo primarii, et capitalis baro scaccarii; ex altera parte barones duo, alii iustitiarii, Dalus et Fordus iuris civiles doctores; ad mensulam intermediate Pomphamus procurator regius, Egertonus sollicitator, Gaudius regius ad legem serviens, clericus coronae, et duo actuarii ... ", in some cases it could derive from the Gens Gauia even if it appears very unlikely, it is also possible, in some cases, a derivation from the toponym Gaudi (AV).
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