You can't gift children like people do puppies. You are noble and kind to offer your home to this child. But, you are wise to be cautious.
You need to know who has LEGAL custody of the child. That could be her aunt. If it is, you're going to have to obtain legal custody or emergency custody. Maybe CPS will place the child in your foster care? None of these options are easy or without out of pocket costs on your part.
Don't operate with someone's self generated, notarized letter of custody. That isn't legal and can potentially cause you much harm. As I said, one can't assign property rights to children like one might do with a car.
You should speak to your state's child protective services agency. They can tell you what must be done for you to get custody of this child.
However, be forewarned, that CPS might take emergency custody of thus child, if her legally appointed guardians have abandoned or abdicated their duties.
You could also speak with an attorney. An attorney could give you guidance and advice about how to obtain emergency custody of the child.
If your funds are tight, and your heart is big, you might not want to try this. The poorest, most destitute, insane couple can breed litters of unfortunate kids. They can keep popping them out, quicker than toast from a toaster. But, attempting to get custody of a troubled kid isn't that simple or easy (as you will soon discover)!
God bless you for trying to help a kid. I hope you don't get hurt in the process.
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