Andrew - I am sorry to read of your loss.
We register the legal ownership so there is no transfer/assent in these circumstances.
The 'shares' and TIC you refer to relate to your beneficial ownerships and we don't record the specific shares on the title. The 'change' in share size is private to you and your sister for example.
Joint property ownership: Overview - GOV.UK
The only application to consider would be to update the register re the death
Documents you need to send
To remove a deceased joint owner from the property record, please complete:
and send either:
Please do not send originals. All certified copy deeds and documents that are lodged with an application will be destroyed following our scanning process and no copy documentation will be returned on completion of the application.
Find out more about Devolution on the death of a registered proprietor.
How much it costs
There is no fee for this application.
Where to send your application
HM Land Registry address for applications.