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Scholten is either patronymic, after Scholte/Scholto/Schelto, thus meaning "son of Scholte" or after a profession, the schout , which translates as "bailiff, sheriff" (he who punishes). The firstnames Scholte, Scholto and Schelto are from schout as well.

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Rant i can't find, but could be from rand , which means "border, edge", which could mean the person used to live near the border, edge of something (like the village).