To relinquish something is to let it go so that someone else can have it — a high job, a right, a claim, power, a title — and the word usually carries the feeling that you did not really want to. You were holding it, and then you had to hand it over. It is a serious, rather formal verb. You read it in news about leaders, courts, and families fighting over rights. You would not usually say you relinquished your umbrella; you would say you gave it up or handed it over. Though actually, people also use it more softly, as in relinquish control in a meeting, meaning stop gripping every decision, even when no crown is changing heads. The unwilling taste is often still there: not a happy gift, a letting-go.