The Muslims voted to be separate and so Pakistan/Bangladesh was formed. Immediately there was fear by Muslims and Hindus so they picked up and left. At the same time, there was sectarian violence helping to "motivate" Muslims and Hindus to pick up and leave.
The refugees from that partition were resettled, for the most part. When Bangladesh broke off from Pakistan, however, a fair number of Bangladeshis wanted to be Pakistanis. Pakistan did this for a while. Then they refused to allow more refugees to settle in Pakistan proper and stranded a lot in India. Some are still refugees.
http://www.usatoday.com/news/topstories/2007-08-14-3079523328_x.htmIn Palestine the partition similarly required no separation of peoples. As with the S. Asian partition that immediately preceded it, the actual partition of peoples followed in short order, and was both voluntary as well as "motivated" by interethnic violence that, as in S. Asia, had preceded partition by decades and involved both some long-standing animosities as well as some more recent ones, resulting from Muslim hegemony followed by a reversal of fortunes as Muslims were no longer in charge.
There were other partitions. In the late '30s, Poland and Czechoslovakia. After WWII, Europe continued what apparently had become tradition: Poland was shifted (and Belorusia expanded), the border between Italy and Slovenia moved, Germany was partitioned, more of the Ukrainian-speaking area was given to Ukraine, Romania was split. There are still Germans calling themselves refugees; Italians, too, I think, in spite of the fact that in the Italy/Slovenian repartition the land taken from Slavs was to be given to the Italian refugees (and was instead kept by the state). I can't take the German and Italian claims seriously since they were assimilated and their "status" is neither one of legality nor of economic disparity, merely one of hurt feelings (and therefore, it seems, utterly meaningless except for purposes of disparaging those so offended).