Jan - it's a common Q to ask and whilst we can direct you to the forms needed to do X or Y it's legal advice you need as to which option is the right one for you and your children
You are correct that you don't need probate as the legal ownership of the property does not form part of his estate. It can though still be used as evidence of his demise.
I should also add that you can still sell the house but you have to account for his beneficial interest/the TIC aspect when doing so. One option is to appoint someone to act with you and together you then sell/transfer to the buyer.
If you decide that you do want to transfer the title to yourself and your adult children then our online assisted guidance will help re the forms and procedure -
HMLR Guide: Start - External · HM Land Registry
If you decide that you want to set up a trust with the children as trustees then our PG 24 offers guidance from a registration perspective -
Private trusts of land (PG24) - GOV.UK
But please do seek appropriate legal/financial advice to understand what options you have, the impact on you/your children going forward and more