What is the Church’s stance on adopting children if you are single and plan to remain single?
So far as I know, the Church doesn’t have a “stance” on the issue. As a matter of prudence though, we could say that adoption by a single parent likely is better for a child than no family at all, but the best interests of the child would be adoption by a traditional married couple. If a single person wants children, he or she should reconsider the possibility of a vocation to marriage.
In other words, what should take precedence are the best interests of children and not the desires of single adults.