As a general rule, the person making the gift or whose estate has bequeathed the inheritance of capital property is responsible for all taxes. Spousal transfers and certain other exceptions exist.
CRA normally considers the giver to have sold the property at fair market value on the date of the transfer to the recipient. Therefore, the giver is liable to pay tax on any capital gains that might arise.
For the recipient, the cost base of the gifted or inherited item also is the fair market value at the time of transfer. This will be used to calculate any future capital gain if the recipient disposes of the property.