So far, three consoles are capable of downloading distributed items. They are the Nintendo Wii, Nintendo 3DS, and Wii U. Therefore, the two games which utilize this feature are Animal Crossing: City Folk and Animal Crossing: New Leaf, since there are no games released for the Wii U.
Distributed items are scheduled to be released usually during a weekly or monthly period, where the item is received within the allotted time. Usually, Pete, the mail carrier, gives the player the items which are attached as presents to letters, upon starting the game and leaving the house by standing outside to get the player's attention. He will mention that the letters are from Nintendo, but some may be signed by special residents or out-of-game characters that appear in other Nintendo games. Other times, if it's not Pete, Wendell will give the player one of his designs to commemorate a special occasion.