Irregular Webcomic! #3619

Tintagel Castle is part of the holdings of the Duchy of Cornwall, which is technically owned by the Prince of Wales. The Prince of Wales is a title granted to the heir apparent to the British throne. Because the British monarchy used male primogeniture until this was changed to absolute primogeniture in 2015, a female heir could not prior to 2015 be the heir apparent, but merely the heir presumptive.^[1] So from 20 January, 1936, when Edward VIII (heir apparent of his father George V) acceded to the throne, until 26 July, 1958, when Elizabeth II granted her then nine-year-old son Charles the title (six years after her accession), there was no Prince of Wales, as Edward had no children, and soon abdicated the throne to his brother George VI, who had two daughters and no sons.

When the title of Prince of Wales is vacant, the Duchy of Cornwall reverts to the Crown Estate, owned directly by the monarch. So given the timeline of this comic, Monty's assertion that Tintagel Castle is Crown property is correct.

[1] Following the 2015 change, it is now possible for a female to be heir apparent to the British throne, and any such female would then receive the title of Princess of Wales, while her husband, if she married, would presumably just be some Duke or other (Cornwall, I guess), and not the Prince of Wales. But we won't find out for quite some time, as the next three heirs in line are all male: Charles, William, and young George. (If Elizabeth II, Prince Charles, and Prince William all died suddenly, Prince George would become king and his sister Charlotte would be the next heir, and the first possible Princess of Wales in her own right.)

The succession rules are complicated enough that I goofed in my example above. Paul S. writes:

You are wrong to say: "If Elizabeth II, Prince Charles, and Prince William all died suddenly, Prince George would become king and his sister Charlotte would be the next heir, and the first possible Princess of Wales in her own right."
Better: "If Elizabeth II, Prince Charles, and Prince George all died suddenly, Prince William would become king and his eldest (surviving) child Charlotte would be the heir apparent, and the first possible Princess of Wales in her own right."
Better still: "If Prince George were to die suddenly, at a young age, followed by Elizabeth II, and Prince Charles, Prince William would become king and his eldest (surviving) child Charlotte would be the heir apparent, and the first possible Princess of Wales in her own right."
The title Prince of Wales is reserved for the Heir Apparent to the throne. Heirs Presumptive are given Royal Dukedoms, starting with York, then Cambridge. The same would now presumably apply to Princess of Wales.
Even if Queen Elizabeth, Prince Charles, and Prince William were all to die (or be disqualified) and Prince George to become King; Princess Charlotte would be only the Heir Presumptive, and could be supplanted at any time by a child born to George (now King George VII). As Heir Presumptive, she would be made a Royal Duchess (probably Duchess of York, unless Prince Andrew were still around).
For Princess Charlotte to become Princess of Wales, Queen Elizabeth, Prince Charles, and Prince George would have to die (as well as any children or grandchildren of Prince George that there might be), but not Prince William, who would become King William V (unless he chose some other name). As the eldest (surviving) child of the King, she would be Heir Apparent to the throne, and could not be supplanted by any later birth.
Other Royal Dukedoms: Windsor and Edinburgh have been granted to royals out of the line of succession, Lancaster is reserved for the Monarch, Cornwall for the Heir Apparent. Queen Charlotte's husband can expect Edinburgh. Earl (or Duke) of Wessex may well pop up again after Edward dies, possibly between York and Cambridge.
And there are parallel Scottish titles for (almost) all these, starting with Lord of the Isles for the Prince of Wales. (or Lady of the Isles for the Princess of Wales).