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Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018
British Dictionary definitions for on someone's behalf

behalf

noun
  1. interest, part, benefit, or respect (only in the phrases on (someone's) behalf, on or US and Canadian in behalf of, in this (or that) behalf)

Word Origin for behalf

Old English be halfe from be by + halfe side; compare Old Norse af halfu

usage

On behalf of is sometimes wrongly used where on the part of is intended. The distinction is that on behalf of someone means `for someone's benefit' or `representing someone', while on the part of someone can be roughly paraphrased as `by someone'. So, the following example is incorrect: another act of apparent negligence, this time not on behalf of the company itself, but on behalf of its banker, when what was meant was there was negligence by the company's banker
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
Word Origin and History for on someone's behalf

behalf

n.

c.1300, behalve (with dative suffix), from Old English (him) be healfe "by (his) side," and on (his) healfe "on (his) side," from healfe "side" (see half).

Online Etymology Dictionary, © 2010 Douglas Harper
Idioms and Phrases with on someone's behalf

behalf

see in behalf of.

The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.