Welfare is money provided by the State (government) to those in society who cannot afford the basic necessities of life. You need to apply for it, and if you don't fit the criteria, you can't get "any assistance from Welfare."
In a divorce situation, one parent or the other is typically "awarded custody" of the children. Or both may have "joint custody" or from time to time, one parent or another party (person) may have "temporary custody." These decisions are made by the family court, and therefore are legal documents, and that's why the reference to signing the papers.
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