Genuine question. If the Monarchy was abolished tomorrow, what would happen to this Crown Estate? Including the 2% of Cornwall gifted to whomever happens to the Prince of Wales at the time.
Those are separate things, the Crown Estate is owned by the Crown, (so essentially the state), if we abolish the crown then the Crown Estate just becomes assets owned by the Republic... change the name to the Republic estate if you like.
The land in Cornwall is owned by the Duchy of Cornwall in order to provide an income to the Prince of Wales's household (likewise the Duchy of Lancaster does the same thing for the King or Queen), I doubt they'd be kept either as they're not privately owned assets and there would be no more King or Queen or Prince of Wales.
Private assets like the Sandringham Estate and Balmoral Estate, the stock market investments, private artworks (not the Royal Collection though) etc... do belong to the King as a private individual (or are held by private trusts for use by him and his heirs as private individuals) and those things couldn't simply be taken.
I imagine there would be very very expensive legal battles over it and in the end some law firm in London would own it all. I don't know honestly. There may be provision for this somewhere in law or the agreement over it all.
In this day and age though you cannot just seize assets because you don't like someone as many in this thread seem to be suggesting.
You wouldn't be seizing assets unless you say went after Balmoral and Sandringham etc..
This isn't anything new, the crown is separate in each commonwealth nation where the monarch is head of state.
If you go sailing in the British Virgin Islands for example you can go visit Richard Branson's private island uninvited... sort of, he owns the island but the land up to the high tide mark belongs to "the crown", not the British Crown but the British Virgin Islands crown.
Similarly, the King is separately King of Canada, King of Australia etc. and you can speak of things owned by "the crown" there. At some point in the future, those countries may decide to abolish the monarchy, Barbados did in 2002 for example.
In your imagination, you envisage very expensive legal battles re: crown assets but in reality, for example, land in Barbados to the high tide mark belonged to the (Barbados) crown... after 2002 it still belongs to the Barbados state but now it's a republic.
The Queen didn't go to court and try to claim it was her private property because it wasn't her private property, it was property belonging to the crown (of Barbados) the very thing they'd just voted to replace with a republic.