"Thank you for your Freedom of Information Request which is repeated at the bottom of this email for reference.
The Crown Estate's property assets are owned by the Sovereign in right of
the Crown, so the ownership passes with the Crown and is not the personal possession of the Monarch or any individual member of the Royal Family.
The Crown Estate's primary role as set out in the Crown Estate Act 1961 is to enhance the value of the estate and the income it generates. The
income surplus generated is paid directly to the Treasury for the benefit
of the UK taxpayer. For more information on the history of the ownership
of The Crown Estate, please visit our website:
[1]www.thecrownestate.co.uk/about_us...
There are no provisions regarding the ownership of The Crown Estate in the hypothetical situation where the monarchy was to be abolished, so I
cannot provide you with any information in that regard."
In other words (to paraphrase) the Crown estates are owned by the "Sovereign". If there is no "Sovereign" then who the fuck knows.
I suspect there would be a compromise agreement reached with a division of assets between the outgoing monarch and the State with a non-compete clause so they can't set up as Monarch of America within say a 6 month period.