Steps when Tenant in Common dies, leaving their share to the other Tenant, in their will

I've read online guidance, but am confused...
Mum and Dad were Tenants in Common, each owning 50% of their house.
Mum died in December. Her will leaves everything to Dad. We are waiting for Grant of Probate.

What LR forms do we need to complete?
It seems clear that one is DJP. After that, I am confused.

Paul - it can be confusing as often most of the things to consider, inc wills and probate, don;t directly relate to what you may wish to do re the registered information
There are two things to consider here. The first you have already done and that's form DJP plus a certified copy of either probate or death certificate. That will update the register re the death.
You also refer to them being TIC and a 50% share each and Mum leaving her share to Dad. So in essence Dad is now the legal and beneficial owner.
When joint owners become TIC they invariably apply to register what's known as a form A/joint ownership restriction. They don't have to but many do. I'm guessing you've checked the register online but if not you can do so for a small fee 
So if the register refers to a form A restriction you can apply to cancel it by submitting forms RX3 and ST5. This is explained in our Practice Guide 6 section 7. Have a read of that guidance and complete forms RX3 and ST5 as appropriate - the jargon may appear confusing but the key is to not over think it and complete the ST5 with the key (bulleted) facts as listed. 

Thanks Adam.

I have not completed the DJP yet, but will do so,

The Title does have a restriction: "No disposition by a sole proprietor of the registered estate (except a trust corporation) under which capital money arises is to be registered unless authorised by an order of the court."
Is that the "form A restriction" that you are referring to?
if so, I will look at RX3&ST5 and the guidance.
Presumably I can do the DJP and RX3&ST5 now, and I don't need to wait for the grant of probate?
Do I need to do anything regarding the transfer of ownership to Dad when probate is granted or does the RX3&ST5 cover that?
Thanks for your help!

Paul - it is a form A restriction and yes you can lodge the forms together.
There's no transfer of ownership involved as the legal ownership, which we register, passes to Dad as the sole surviving registered owner.
Probate for Mum isn't needed re the property itself as the property doesn't form part of her estate. So with regards the property alone probate is not required. But you may need it for other reason(s)

Thanks Adam.
The bit about the house not being part of Mum's estate confuses me, but I guess that's not relevant to the completion of the forms, so I'll ignore that for now. 
We have completed the forms and will get them in the post to you.

Paul - it's the bit that often throws people but it's the distinction between the legal and beneficial ownerships that matter here from a registration and legal perspective. The easiest way I find to describe it is if you think of the legal ownership as all the land plus bricks & mortar and the beneficial ownership as the value, the £s and pence, of that land plus bricks & mortar
We register the legal ownership and that is always dealt with as a whole - you can't split the bricks & mortar and have half a kitchen each, and half a bathroom etc. So when you have joint registered owners they own the whole of the legal ownership jointly. And when one of them sadly dies that whole legal ownership passes to the surviving owner to deal with 
The £s and pence can though be split as you can have £100K each of a £200K house. And that beneficial ownership/share can be left to someone else.
But the legal ownership has passed to the surviving joint owner so the property, which we register, does not form part of the deceased's estate and probate is not needed to deal with the property
The beneficial ownership/share still exists but how that's then dealt with depends on a number of possible factors inc the split, trust, wills and wishes of beneficiaries and surviving owner. We don't deal with those complexities and how matters are then resolved (or left) depends on those involved. We simply register any change to the legal ownership as and when that happens. What discussions and arrangements are made to get to that update isn't something we are involved in
Hope that helps

I see now. Crystal clear. Thanks!