All three used a mid-2016 estimate of 25.8 million as a baseline, but assumed different future migration rates.
A revealing survey by Pew Research Center, "Europe's Growing Muslim Population", looks at the future of the 25.8 million Muslims now residing in European countries.
While Muslims made up 6 percent of Germany's population previous year, their proportion would go up to 20 percent by 2050.
A major conclusion is that even if all migration into Europe were to stop ("zero" migration scenario), the continent's Muslim population would likely rise from the current level of 4.9 percent to 7.4 percent by 2050 - because on average Muslims are younger and have higher fertility than other Europeans. In the high migration scenario, Germany and Sweden would have the biggest increases because both countries took in the most asylum-seekers during the height of the refugee crisis two years ago. "Levels of religious commitment and belief vary among Europe's Muslim populations", the report said. Sweden's Muslims, who were at 8 percent in 2016, would account for 31 percent of the population in that same scenario.
However almost half of all migration into Europe (47 per cent) was not Muslim, with Christians making up the next largest religious group, meaning that migration mitigates somewhat Christianity's decline.
The researchers said that is mostly because Muslims are on average 13 years younger than other Europeans and also have a higher birthrate, the Pew researchers said.
A second, "medium" migration scenario assumes that the flows of refugees stop, but "regular" migrants continue to come for reasons other than fleeing wars and instability.
The report found that Germany was the top destination for Muslim refugees between 2010 and 2016, whereas the United Kingdom took in the highest number of regular Muslim migrants.
The research centre sets out three different projections for the coming decades, according to varying estimates of future migration levels. Even if all current 28 European Union members, plus Norway and Switzerland, closed their borders to migrants, the Muslim population constituent in the west would continue to grow because of a younger age profile and higher fertility rates, but would remain very low in the east.
Migrants arriving in Munich, September 2015.
Even under its "high" migration scenario, Pew projects a Muslim population of 4.5% of the total population for Hungary, 1.2% for the Czech Republic, 1% for Estonia, 0.9% for Romania, 0.7% for Slovakia, 0.4% for Latvia, and 0.2% for Lithuania and Poland. Even with "high" migration, Poland's Muslims are expected to total no more than 60,000.
Also the Swiss census from 2000 showed that the birth rate among integrated Muslims had fallen.
The study would also appear to give the lie to some claims from Europe's far-right, which has been gaining ground in several countries. The continent's Muslim population has grown by over 20%, or 6.3 million people, since 2010.
The Pew Research Center report, published on Thursday, modelled three scenarios for estimating the number of Muslims who will be living in Europe by 2050.