Thanks for your question.
If she does not have leave to remain then you can inform the UKBA of her, giving her details of how she came her citing the fact that she is an overstayer and asking them to consider deportation. You can contact them through the details on the following link:-
If they find that she is illegal and detain her then she will probably receive a 10 year ban if she is deported at the cost of the state. Her identity can be traced by the perons at the UKBA dealing with deportation issues.
The child is eligible to be registered as a UK citizen if you are a UK national. This creates problems in that she could register the child as such and then potentially seek to secure leave to remain on human rights grounds by virtue of the child's UK citizenship. This is not easy however and she would certainly need to pay a solicitor to make the application on her behalf.
If she secures leave to remain here then she could seek child support from you at the rate of 15% of your net weekly income.
If you attempt to serve reasonable notice on her to vacate your property (ie. Because she has been there under licence effectively) and she leaves then fine. If she does not you would need a court order to evict her and that will not be easy to obtain because the primary concern of the court will be the welfare of the child because you are the father.
Basically, you have to contact the UKBA if you want her deported. You will need to give them as much detail as you possibly can.
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