Where is the text you're relying on? Secondly, the British, at the time of the Declaration ("understood, at the time of the Balfour Declaration, to be the whole of historic Palestine, including Transjordan") understood that, not by 1937 which by then they had already turned their backs on the "National Home" concept. You're misreading the quote.
So I ask you again: show me a single document, British or League of Nations, that says the Jews are to receive all the land of Palestine for a state.
You are misreading the document. It speaks about not prejudicing the civil or religious rights of the others there, i.e., those who would live under the "National Home for the Jews". In other words, not prejucing what would eventually become minority interests in the "National Home" because of Jewish immigration. The "National Home" in the entirety of the British Mandate is exactly what Balfour was referring to. "Palestine" was understood in law to be both areas East and West of the Jordan. I don't see why that is difficult for you to understand.
Follow the links in the webpage you referenced as a source.
Secondly, the British, at the time of the Declaration ("understood, at the time of the Balfour Declaration, to be the whole of historic Palestine, including Transjordan") understood that, not by 1937 which by then they had already turned their backs on the "National Home" concept. You're misreading the quote.
I'm not misreading it. I'm questioning where it comes from. The website you referenced claims it was in the Peel Commission Report. I followed the link to the report and could not find the quote in the report text.