What is 'adopt as care dependent'?

Basically the same as it was before, but its a way of distinguishing that the child is adopted.

It came in the toddlers patch. Its just a carer I think. It only shows up if the child doesn't have a parent I think

It's a way for a non-biological young adult, adult or elder (related or not) to take special care looking after the needs of a child or toddler (and teen, I think). It doesn't necessarily mean the child is adopted using the adoption mechanism. The carer could be a grandparent, older sibling, etc.

In my game it came up for the toddler whose mother lived outside the household. His brother, also a toddler couldn't get her for caregiver. But that might be because he picked his uncle for this role. So, I think only one person can take on this role.

Hm... because the children in this household have two biological grandparents and a father.

My current family is a man, his twin brother, his wife and his toddler. So the toddler does have both parents living in the house, but the Uncle did also get this option.

Must be an option for any non parent, I guess.

There are some limits it seems. Sims can't just "adopt" a random child. My sim can't adopt his ex-girlfriends (teen) daughter.
They might have to have a relationship somewhere on the family tree for it to work.

Yeah it showed up with my (toddler) sim while playing as his grandmother. Its just so that a non-parent sim can assume parenting responsibilities and aid in raising a child.

The claiming as "dependent" thing should be available to any Sim in the household YA and up: http://forums.thesims.com/en_US/discussion/comment/15765660/#Comment_15765660