There is no standard answer for this question, beyond the general one that most children and male-line grandchildren of European sovereigns, excluding 'sovereign' counts of the Holy Roman Empire, were princes and princesses, even if their titles were translated into English differently, or other titles preferred; there are a few exceptions (e.g. some of the junior Wittelsbachs were titled as Dukes and Duchesses in Bavaria). On a case-by-case basis: 'Infante/a' was employed in Spain and Portugal for children of the king, and sometimes male-line grandchildren; it's appropriate to translate it as prince/ss. The title of Archduke came about when the Habsburg duke Rudolf IV of Austria forged a document in 1358, outlining special privileges due the Habsburgs in Austria; this Privilegium Maius was ignored by the reigning Holy Roman Emperor, but eventually accepted as genuine -- in 1453, once Frederick V of Austria had managed to become the Holy Roman Emperor. 'Grand Duke' is a translation of the Russian veliky kniaz into English, although 'Grand Prince' would be more literal, and the title is unrelated to the sovereign title of grand duke, or, for that matter, any kind of duke. The Germans, for example, translated it Großfürst, which is literal, whereas an Austrian archduke was an Erzherzog, or literally an archduke, fürst and herzog meaning prince and duke respectively, although the use of fürst instead of prinz in the case above was exceptional.
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