It depends on where you live - England is different to Scotland, for example, and how much money is involved.
Assuming England and under �200k
If there is no husband or wife - parents share equally;
No parents - brothers and sisters share equally
No brother and sisters - half brothers and half sisters share
No half brothers and sisters - grandparents share equally
No grandparents - aunts and uncles share
No aunts and uncles - the Crown gets the lot
Now, in your scenario there are nieces and nephews, which means there must have been brothers and / or sisters, or at least one sibling.
The assets are divided amongst the brothers and sisters as if they were alive, and from their apportioned to the nieces and nephews.
To keep simple - estate is worth �100,000 and the deceased had one brother and one sister, now dead. They would be entitled to �50,000 each. The brother has a son, and the sister two daughters. The nephew gets his share of his father's legacy - �50,000; the nieces get equal shares of their mother's - �25,000 each