Marie - I am sorry to read of your loss. We can't advise you on what's 'necessary' in such circumstances as we register the outcome of such decisions and it's legal advice you all need, which we don't give.
One option is to leave it as is until a sale or later death
As you were joint owners probate is not required re the property as the legal ownership passes to you to deal with and does not form part of his estate
If you decide to transfer the property into your joint names then you will have to apply to update the register as appropriate. The house does not transfer automatically to any beneficiaries. You would have to transfer it to yourself and them if that was the decision made.
I would recommend seeking legal advice or speak to whoever advised you on your wills/trust as perhaps what might happen next and the impact of same was discussed
Our online assisted guidance will help you to identify the forms and more needed once you have decided how to update the register
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