Adoption agencies adopt pets and increase their skills or change their styles and then put the "improved" pets up for adoption again. Sometimes guilds do this as a project for members or for Neopians at large. It helps if you or a member of the guild doing this have a lab ray. You cannot pick who can adopt a pet, but you can make it easier for a particular person to get one by arranging to put it up for adoption at a specific time and letting the person know the exact name of the pet.