Summary

Yosef Karo Shulchan Aruch — Yoreh Deah 120 The Laws of Immersion of Vessels

And there are those who disagree and say to dunk without a blessing. And if some of the silver used to make the vessel was owned by the idol worshipper, dunking is required. And thus an Israelite artisan who makes a vessel for an idol worshipper and acquires it from him shall dunk, also without a blessing if the idol worshipper gave him the metals, but if [the Israelite artisan] makes it himself and only acquired the metals from the idol worshipper or if he gave some metals of his own, dunking is not required.
Source: Wikisource

Yosef Karo Shulchan Aruch — Yoreh Deah 120 The Laws of Immersion of Vessels

One may not believe [ie rely on] a child regarding dunking of vessels. (GLOSS: But if [the child] dunks before an adult, it is considered a dunking) .
15 אם הטביל כלים על ידי עובד כוכבים עלתה להם טבילה. (אבל אינו נאמן על הטבילה) (ד"ע) : If one dunked vessels alongside an idol worshipper, it is a dunking (GLOSS: But one may not believe [ie trust] [an idol worhsipper] regarding dunking) .
Source: Wikisource

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