Where the parents give a gift to their children they are deemed to have "disposed" of it at market value. This is a chargeable event for CGT purposes. The actual CGT is calculated by difference between the market value at disposal and the original cost of the asset with all the usual charges allowed ie indexation, selling, buying expenses, annual allowance, etc
Note that if CAT and CGT liabilities arise from the same event ie a gift, the CGT can be used as a credit against the CAT liability
The child is deemed to have received the asset at market value and this will be used to calculate his CGT liability if/when he (the child) disposes of it in the future.
Note that if instead of gifting the asset to the child whilst alive, the asset is passed to the child on death (either by will or through intestacy) there is no liability to CGT.
CGT is paid by to the person/estate disposing of the asset
CAT is paid by the receiver of the gift/inheritence