I must confess, this post is rather late. We first saw the קצוה"ח on which it's based last Thursday night, but until tonight (Mon), I didn't really have a clear enough understanding in everything to feel comfortable letting anyone see my (limited) understanding. Thanks to some clarifications in today's שיעור and a discussion with my חברותא, I now feel I understand this fairly well.
The שולחן ערוך writes that מחילה works without any קניין required. That is, if Reuven owes Shimon money, and wants to forgive the debt, he can do so without any formal מעשה קניין. There's a discussion amongst the פוסקים whether this is true if Shimon has a שטר testifying to Reuven's deby.
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