Тhe rule is that they get a share of one third of the moveable estate, so they wouldn't be able to claim houses, for example, or land. (Jewellery and cars count as part of the moveable estate.).
Any bills and funeral expenses, etc have to be paid out of the moveable estate first, so that reduces the amount. It would also be possible in theory for someone to give a significant amount of their estate to their spouse before dying, if they knew that their spouse was likely to outlive them.
There are Scottish law firms which advertise that they can formulate some kind of trust in order to avoid giving money to children, but I'm not sure how that works.
I do have a friend who has become estranged from one of their adult children. I don't know the full story, but I believe that the child behaved in an unacceptable manner towards another adult child who became terminally ill. (So far as I can tell, this was not a case of 'golden child' syndrome - there are other children and grandchildren and they are all supportive.)
They have done everything possible to disinherit the child who behaved in an unacceptable manner. That child's share will be going directly to their children, thus skipping them. The deceased child's share will be going to their own children, of course.
As I said, I don't know exactly how it works - I've never been in a situation where I've had enough money to make it worthwhile for me to contact a high-powered chartered accountant or solicitor.
I did have the help of a solicitor when I was my husband's executor and he did want to write the letter mentioned by a previous poster, asking whether they wanted their legal rights.
I told him to change it to something along the lines of "The enclosed cheque constitutes your legal rights", but I believe he added a paragraph saying that cashing the cheque meant that they accepted that this was their legal entitlement. They were also sent family jewellery and medals, but these had to be valued first.
I never did see the letters that were written - I only signed the cheques as executor. My understanding is that such letters are written to a particular formula.
There was also a cheque sent to an adult grandchild, but no deed of variation was required since this came out of my inheritance, rather than the estate as a whole. (My husband had told me how much to give the grandchild.) I also passed on some family jewellery to the grandchild. Again, no deed of variation was required for that.