The State determines what happens to the financial assets of someone who dies with no Will at all.
The current rules set out a “decision tree”, branching in different directions depending on the answers. https://www.gov.uk/inherits-someone-dies-without-will/
In essence, the people who would inherit (in order) are: spouse and children, then parents, siblings, grandparents, uncles/aunts, cousins, great-grandparents, great-aunts/uncles, more distant cousins, and so on. Half-blood relations take precedence over the next full-blood category.
There are rules about how much is inherited between spouse and children, but thereafter the numbers of members of each group will determine the share of the estate.
So if you have a large family, or your grandparents did, you ought to consider making provision for the individuals you wish to benefit rather than let your estate be divided in increasingly small shares.
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