Hi Figgy, found this on Solo.ie tried to copy the link but couldn't get it to work so pasted instead, its a great website for Single Parents it may help with your query and as it says below it is not legal advice just information only:
Your childs inheritance rights
All children have the same basic rights under succession law, whether or not their parents have married each other, and 'children' here includes adult children as well as minors. What these rights are depend primarily on whether the deceased person has made a will or not. However, a child whose parents have not married each other may have difficulty asserting those rights with regard to her/his father or people related to her/him through the father unless s/he can prove paternity. If paternity has been established either through the name being entered in the Birth Register or with a court order (see section Establishing Paternity) during the fathers lifetime, this difficulty is largely done away with. If paternity has not been established before the father's death, there may be difficulties of evidence and proof afterwards.
Where no will has been made
If either of the child's parents dies without having made a will, and leaves no spouse and no other issue (i.e. children or grandchildren) the child will inherit the entire estate. If there was no spouse but there were other children then each child (whether born within or outside marriage) is entitled to an equal share. If the deceased is outlived by a spouse, the spouse is entitled to two thirds and the child (or children) to the other third, divided equally between the children. Where a relative (other than the parent) of a child dies without having made a will, the child may be entitled to share in the estate, depending on what other closer relatives may have survived the deceased.
Where a will has been made
Where the relative who died has made a will, the terms of the will are put into effect. There is no obligation on a person making a will to make provision for any or all relatives whether born within or outside marriage. However, if a parent who died having made a will failed to make proper provision for any of his or her children (including children born outside marriage, and adult children), then the children affected may apply to the court for a share in the estate. Where a will is made after 14th June 1988 which uses any terms which describe a family relationship (e.g. 'child', 'grandchild', 'cousin'), the law interprets such terms without regard to whether any person's parents had married each other, unless it is clear from the context that the contrary was intended.
Making a will
If you are over 16 years it is advisable to make a will as it makes the settlement of your affairs easier for those who survive you. Even if you have not much by way of property to dispose of, making a will gives you an opportunity of appointing someone to act as your child's guardian after your death (see section Guardianship, Custody and Access). Take legal advice before making a will.
The material on these pages is for information only and is not legal advice.