If the Jewish state is autonomous, then it can open itself to unlimited Jewish immigration. Several hundred thousand Jews will arrive in the next few years, roughly doubling the Jewish population in
Palestine.
Another question is who or what controls migration between the Jewish Zone and the Jerusalem Zone.
If there is no effective restriction on Jewish settlement in Jerusalem, the Jews will occupy that area as well.
And also, does alt-Israel have its own armed forces of any kind, even a gendarmerie? ISTM that alt-Israel would need such a force for defense against Arab raids. If the Jews have any sort of army, their position becomes much securer. It would be under British supervision, of course, like the Arab Legion.
Speaking of which, the Legion was the only official armed Arab force in Palestine. Abdallah of Trans-Jordan wanted to add Palestine, or the Arab parts of it, to his kingdom, and he has a fair amount of leverage. Unless the Palestinians actually cooperated with British in establishing their own state in their zone, and I don't see either the Grand Mufti or Fawzi al-Kaukji doing that, Abdallah may get his way. The Zionists would accept that.
Nothing violent can happen until the British leave, and they won't leave till after the war. But there will be miscellaneous squeezing and pushing.
The "condominium" of Jerusalem will be unstable, with the population becoming largely Jewish and seeking union with Israel. Abdallah can't consent to that, but there could be a face-saving partition of the Jerusalem Zone, with the Arab Quarter and Temple Mount becoming an Arab enclave (except for the Western Wall).
If the Palestininians form up on their own, and exclude Abdallah... then down the road they might want to try something. But they would facing an alt-Israel with a considerable population (probably larger than Arab Palestine) and a well-equipped veteran army. (There would definitely be a Hebrew Legion in Eighth Army.) And the other Arab countries wouldn't have an excuse to intervene... Except maybe if Israel annexes Jerusalem.
