I have heard many of my friends during discussions about the current conflict in Israel/Palestine about the legitimacy of claims to the land, and several of them said that the majority of Palestinians were simply arabs who immigrated to to the region of Palestine in the mid-19th century. I have had other friends who went to Palestine talk with Palestinians who claim that their family had been had lived in the same village for 8 centuries. What do the Historical records tell us about demographics in the region and how well do these separate but related claims meet historical fact?
You should check out the ongoing AMA in this sub on Israel/Palestine. I believe the OP answers your question.
It's hard to estimate on the basis of Ottoman records, pre-Mandate. The records were not good as far as immigration, we can only see population growth, and we can't determine how much was due to higher or lower birth rates as opposed to immigration. The best records we have are during the Mandate period, which is between 1921 and 1933, since there were two censuses during that time:
Part of the problem with what you're asking is that prior to 1922 and 1931 (the two censuses we have and consider credible) there really isn't much besides educated guesses to go off of. However, the British Royal Institute for International Affairs before WWII estimated that the number was impossible to determine (insofar as Arabs entering illegally from Transjordan and Syria), but likely considerable. The two censuses, examined closely, show that there was a growth between 1922 and 1931 in the Arab population of 141,000 or so, from 322,000 to 463,000, from both natural growth and immigration. It should be noted that this was the considered growth in pre-state Israel, as in the territory Israel would later come to encompass after the 1948 War. Other than pre-state Israel, growth was 70,000 people. Unlike in pre-state Israel, the growth in the remaining areas was almost all natural, according to one author, with only some 5,500 people being unaccounted for and likely immigrants. We can, surprisingly enough, find records on the natural growth rate during the same period, which placed the likely population off natural growth alone at around 398,000, meaning the rest (minus about 10,000 due to a transfer of territory between districts) of around 54,000 was due to inter-Arab immigration. During the same period, roughly 94,000 Jews immigrated, placing Arab immigration at being around 36% of all immigration into the area between 1922-1931. The British, however, estimated in other official reports that the growth was all natural. In 1937, the Peel Commission wrote that "...unlike the Jewish [community], the rise [in Arab population] has been due in only a slight degree to immigration." They also, in that report, estimated that the increase in population growth was due to increases in health and less conscription since WWI.
I wrote this in another answer, just yesterday, so I figure it's OK for me to put here! I detail the growth of Palestinian identity here in a previous answer as well, which I hope you'll find interesting and comprehensive about what you're discussing :).
One of the issues with trying to determine who had historical "rights" to the land of Palestine/Israel is that you have to pick a time period at which to base your opinion and also decide on what "rules" apply to how that land is governed. Anything before the time period becomes moot and anything after must be consistent with the "rules".
The fact is, a lot of people can claim the land over its 4000 year history of various rulers and empires and conquests, and to make exceptions for one time or another begs the question of the legitimacy of many other nations who's origins may be based on similar rules from a similar time.