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1.
To proclaim or declare to be no longer one's own, to disclaim, disown, cast off; esp. to disown or disinherit children. Now only as a tech. term of Rom. Law (L. abdicare filium, also patrem); To depose (from an office or dignity). Obs.; refl. To formally cut oneself off, sever, or separate oneself from anything; esp. to divest oneself of an office (L. abdicare se magistratu). Obs.; trans. To put away, cast off, discard (anything). Obs.
1541 ELYOT Im. Gov. 149 The father..doeth abdicate nowe and then one, that is to saie, putteth them out of his familie. 1644 MILTON Jus Pop. 34 Parents may not causelessly abdicate or disinherit children. 1697 POTTER Antiq. Greece IV. xv. 351 (1715) Parents were allow'd to be reconcil'd to their children, but after that could never abdicate them again. a1763 SHENSTONE Essays 117 Wherever I disesteemed, I would abdicate my first cousin. 1828 SEWELL Oxf. Pr. Essay 70 Sons were exposed, abdicated, and sold by the laws of Solon
by JDOE October 18, 2002
 
2.
to remove oneself from being head of state. eg. Queen/King.
Mary Queen of Scots was forced to abdicate the throne by rebels. She was no longer Queen of Scotland, and her son became King.
by Vaughn January 13, 2005
 
3.
To give up all hope of ever having a flat stomach.
A: No more workouts ?!!
B: No, I abdicated :(
by LaneDevilishAngel March 22, 2011