Adoption Papers allow you to claim a spirit from the Adoption Center even if you own characters already. The higher rarity the geno, the more Adoption Papers you'll need to claim it. You can get one a month for free in Gaia's Giveaways.
Common → 2
Uncommon → 4
Rare → 7
Legendary → 10
Unique → 14
You can claim a geno via admin requests, you must have no undesigned genos to claim one. (Does not include Centaurians or Customs/Transfers in small quantities) Make sure to attach the needed papers.