The Collaborative International Dictionary of English v.0.48:

Relinquish \Re*lin"quish\ (-kw?sh), v. t. [imp. & p. p.
   Relinquished (-kw?sht); p. pr. & vb. n. Relinquishing.]
   [OF. relinquir, L. relinquere to leave behind; pref. re- re +
   linquere to leave. See Loan, and cf. Relic, Relict.]
   [1913 Webster]
   1. To withdraw from; to leave behind; to desist from; to
      abandon; to quit; as, to relinquish a pursuit.
      [1913 Webster]

            We ought to relinquish such rites.    --Hooker.
      [1913 Webster]

            They placed Irish tenants upon the lands
            relinquished by the English.          --Sir J.
                                                  Davies.
      [1913 Webster]

   2. To give up; to renounce a claim to; resign; as, to
      relinquish a debt.
      [1913 Webster]

   Syn: To resign; leave; quit; forsake; abandon; desert;
        renounce; forb?ar; forego. See Resign.
        [1913 Webster]

WordNet (r) 3.0 (2006):

relinquishing
    n 1: a verbal act of renouncing a claim or right or position
         etc. [syn: relinquishment, relinquishing]
    2: the act of giving up and abandoning a struggle or task etc.
       [syn: relinquishment, relinquishing]