Currently I have had a three year old girl living with me since September. I have no legal documentation from her mother that temporarily gives me custody. I am not related to the child. The mother is pretty much homeless, she randomly rents rooms that are not in the most child friendly settings. She does not have a job. She has not provided anything for the child in the time that I have had her. What can I do?

Ask the mother to turn guardianship over to you. You can always attempt to prove that she is an unfit parent but that doesn't guarantee that the child will be transferred to your custody/control.

A parent is unfit when she places the child in substantial danger of any sort.

Another thing that isn't mentioned here is the Father of the child ? If you try for custody then he will be involved in some way. If you follow what judy has said then the father doesn't have to be involved and if needed you can care for the child's medical needs. Right now your stuck.

Yes you are stuck, you might even be charged with kidnapping. You just can't keep a child without legal documentation. A 3 yr old needs regular checkups and you can't authorize care without documentation.

You need to either get social services involved and offer to foster the child, or get the mother to sign over guardianship. But that would need to be approved by a court.