Hi,
Gifting an asset, or a share of that asset, to another person, generates a capital gain. If the property was your mother's main residence, from the date she acquired it initially, up to the date that she gifts you 50%, then Private Residence Relief will absorb any capital gain that arises and no tax will be payable. You can see guidance here:
HS283 Private Residence Relief (2024)
Thank you.