Hi,
Your parent's may have a capital gain liability, as they have disposed of their share of the property. You can see guidance here:
HS283 Private Residence Relief (2024)
There is also a Capital Gains Tax calculator here:
Tax when you sell property
You have acquired 100% of the property in two parts. If you dispose of the property, you would need to obtain the value of the property on acquiring your first share and again when you acquired the remainder. This will allow you to calculate your acquition cost.
Thank you.