It may be possible in some countries in continental Europe. Ancient Roman law did allow for adult adoption and the civil law in force in continental Europe is descended from Roman law.
This story suggests that German law does allow for adult adoption.
This
Yahoo Answer suggests that the expectations for adult adoptions (listed below) are more restrictive compared to child adoptions.
The expectations for adult adoption (in general) are;
- to be legally related to the person you are adopting (filiation)
- for them to be your legal heir
- for a parent-child relationship to already precede the legal one.
As you can see, generally adult adoptions are done for family members who are already related more distantly (step-children, nephews/nieces, etc), but who have a relationship more akin to a parent-child relationship.
Adult adoption of a relative stranger to the family may be more difficult.
I am not a lawyer or immigration advisor. My statements/comments do not constitute legal advice. E&OE. Please do not PM me for advice.