Synonyms of 'cough up'
▷ See cough
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If you deliver a person or thing into someone's care, you give them responsibility for that person or thing.
He was led in handcuffs and delivered over to me.
Thesaurus for cough up from the Collins English Thesaurus
If you cough up an amount of money, you pay or spend that amount, usually when you would prefer not to.