> The thing coming closest to a successor state would be modern-day Turkey, I believe.
Turkey rescinded all territorial claims to the area in 1921 or 1922 (I don't remember which).
That's quite the problem, because the Brits had no territorial claim to the area, they only administrated the Mandate. The Jordanians occupied the West Bank from 1948-1967, but it was considered an occupation (like Israel has now) by all states in the world except for Iraq (the Iraqi king was the brother of the Jordanian king). In any case, they rescinded territorial claims to the area in 1991 or 1994 (I don't remember which).
So Israel is currently occupying an area that no state has claim to. And to be fair, Israel has been trying to get rid of it more or less since 1994. Every time they get close some incident or another prevents that - and now the current leadership seems disinterested in getting rid of it.
Formally through the Treaty of Sèvres and Treaty of Lausanne: https://en.wikipedia.org/wiki/Treaty_of_S%C3%A8vres
The thing coming closest to a successor state would be modern-day Turkey, I believe.
Creation of Mandatory Palestine (under British rule, but not considered a state) was a part of the partition.