Players picked up off the wire are brought in relative to your point in the season, so, for example, if you picked up a pitcher after 81 games, he would be brought in roughly half-way 'used up'. This is by design to keep owners from using the waiver wire to refresh their players.
Note: If you pick up a player you have previously dropped, it either will prorate their fatigue numbers based on how far you are into the season or take them as fatigued as they were when you dropped them, whichever is greater. This is to prevent teams from dropping a player and picking them back up to basically erase their fatigue.
Limitations: In Full Season leagues, you have unlimited transactions (release-claim) per season. Your roster can not be modified after the 'roster set date' which is displayed in your GM's Office. Also, you may not waive the pitcher scheduled to start for you that night. For Spring Training leagues, you are limited to 2 transactions per season. For both types of leagues, you must pay a 10% transaction charge for each player that you claim. For example, if you want to claim a 1 million player, you'll need to give up 1.1 million.