Following up on B's reply: If one person puts in a claim, that person gets the player. If more than one person does, whichever of them is highest in the current priority gets the player. Either way, once you successfully claim a player on waivers, you then move to the back of the line in terms of priority. The initial priority order is the inverse order of the last round of the draft (continuing the snaking draft scheme). Finally, if nobody claims the player during the waiver period, the player then becomes a free agent and from then on it's first come, first served. If you claim a player as a free agent (as opposed to on waivers) you keep your current position in the waiver line rather than moving to the back. The person who placed Barrett on waivers can't withdraw the action; however, I believe she could put in a claim herself and it would depend on where she is in the waiver priority relative to anybody else putting in a claim. It wouldn't make much sense to do that, however, since first she risks losing him and second, even if she can claim him back, she'd move to the end of the line for future waiver claims. This isn't like real baseball where teams can place players on waivers to guage possible interest in the players, then pull them back if claimed.