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Promotional adoptables are special in that they're limited in number and can only be acquired through special means. Promos can be given away as contest prizes, consolation prizes for contest participants, just being around on the right day, or even found randomly while performing certain actions.

Contest Promos
Promotional Smeargle This Smeargle is among the most difficult promos to find. It was given away as a consolation prize in the Design a Pokemon Contest run in October 2007.
In the Pokemon Brawl contest, similar to the popular reality show Survivor, members of the winning tribe got these adoptables as prizes.
Brawl Gastrodon (East) Brawl Gastrodon (West)
Promotional Tyranitar Promotional Salamence Promotional Garchomp Promotional Dragonite
These four dragons are given away as prizes in various contests, including the Dinomon Dilemma contest, Trainer Card contests, and the Fansite contest.
Promotional Chaos Neutral Chao This Chao was given to those people who correctly guessed in advance that the advent calendar Chao for December 9th was Dark Fly and Swim.
Promotional Tails Chao This Chao was given the winners of the Missing Chao Contest. Only 20 were ever released.
Promotional Chaos Devil Chao This promo adoptable was distributed to those who participated in the Dinomon Dilemma Contest.
Blog Shiny Lucario Originally the non-shiny version now available through random chance, this Lucario was given to members who were featured in the no longer updated PokePlushies Blog.

Random Chance Promos
Promotional Mew Everyone had a small chance of finding a Mew when leveling up adoptables. This as now been replaced by Lucario.
Promotional Lucario Originally given to those featured in the blog, Lucario can now be found randomly when leveling up adoptables, with worse odds than those of finding Mew in the past.
Promotional Amy Chao This Chao can be found only on Thursdays while leveling up adoptables. The chances of finding one are greater than those of Mew and Lucario, but still not very likely.
Promotional Yoshi are found by posting in the forum. If you're lucky, you will receive a private message saying that you ahve found a mysterious egg. This egg will hatch into a Yoshi at approximately level 50-100. The most common Yoshi is the green, and the Baby Mario Yoshi is the most rare.

Milestone Promos
100,000 Adoptables Knuckles Chao Knuckles was given out to commemorate reaching 100,000 adoptables adopted.
5 Million Hits Jet Chao Jet was originally released in celebration of 5 million hits to the website, but after some people adopted hundreds, and also after some people kept refreshing the site continuously to get the counter there faster, Jet was removed. Thanks, guys.

Other Promos
New Server Promotional Uxie Uxie was given away to celebrate the move to a new server, but was deleted not too long afterwards due to rule breakers. The accouncement regarding the adoptable specifically said 1 per player, but some people thought that rules didn't apply to them and adopted as many as 223. As a result, all uxie promos were deleted.