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You can exclude whoever you like from your Will, this is your right as a testator.
If a person considers that they should have received some part of your estate after you have passed away then they would have to make a claim against the estate under the Inheritance (Provision for Family and Dependent) Act 1976.
The Court will consider what is a "reasonable financial provision" (if any) and will take a number of factors in to account in determining what is fair (eg. size of the estate, other claims, resources and needs of other family members/dependants, responsibilities the deceased had to you), each case turns on it's own facts and there are no hard and fast rules to work out what you are entitled to.
In my view if you have no relationship with the child and do not build any kind of significant relationship with the child (including not giving the child any money) then the mother/child would be on very shaky good making such a claim and would be unlikely to be successful.
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