Hi,
There are a few potential problems if the parent of unmarried children dies.
If the mother of the children dies, and the father is not the childrens legal guardian ( which is not automatic), the father does not automatically begin the childrens guardian, because he is not the mothers next-of-kin.
This can be messy, if the mothers parents get involved. You really need to sort this out.
In the case of inheritance, if one of the parents dies intestate, their children will inherit everything, and the surviving partner will get nothing.
Again, making a will is very important.