The position, role, or responsibility of being a guaranteer or the agreement involved in making a guarantee.
From guaranteer plus the suffix -ship, which creates nouns describing a position or status (like leadership, friendship). The term formalized the legal role in English.
The -ship suffix originally meant 'condition of being' in Old English, so guaranteeship literally means 'the condition of being one who guarantees'—it's a title of responsibility!
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