Practical example:
The daughter of sister of DH's grandfather died intestate. Her parents were dead, her sister, who had no children had died and she also had no children.
The search for relatives started with her parent's siblings (4 of them). They had all died, BUT they had all married and had children. So the money was divided in equal shares between the deceased brothers and sisters (a quarter each), then because they were deceased, their share was divided equally between their children.
In the case of DH's grandfather, most of his children had also died so his quarter was divided by the number of his surviving children plus deceased children who themselves had children, 8 in all. So DH's mother received an eighth of the quarter he inherited. As she had died and DH was an only child he got all her share, but if he had had, say, 1 sibling, they both would have received half of her share.
As the estate was small and the solicitors costs for hunting all beneficiaries was quite high we finally received a cheque for £169.52.