The noun form of 'relinquish' is 'relinquishment'.
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To relinquish something means to let it go. You can relinquish a
debt that someone has to you. But if you have a debt to someone
else, you can't relinquish that, You owe that money to them.
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"Relinquish" in Spanish can be translated as "renunciar" or "ceder".