Helen - if you were joint owners, TIC or not, and you now wish to transfer it then it would be a Transfer by you to yourself and your Mother. The legal ownership is always dealt with as a whole so does not form part of his estate so probate isn't required with regards the actual transfer. It can still be used to evidence his death as part of any application you submit
See our online assisted guidance to help identify the forms and more if you do wish to transfer the legal ownership -
HMLR Guide: Start - External · HM Land Registry