There are warnings that some of the 55,000 "unexplained" moves by pupils between schools in England over five years could be driven by schools trying to remove difficult children.
The Education Policy Institute has looked at cases where pupils have changed school without moving home.
Almost a quarter of these moves have taken place in 330 secondary schools.
David Laws, chairman of the think tank, said it raised concerns "whether some schools are 'off-rolling' pupils".
"The size of unexplained pupil moves is disturbing," said Mr Laws, a former education minister.
What is 'off-rolling'?
This is where schools try to remove pupils with challenging behaviour, or whose poor exam results might damage league table performances.
Schools are accused of wanting to get them "off their rolls" so that they become someone else's problem.
It can be hard to prove, because it might be not be clear whether such moves are the result of schools pushing out pupils or choices made by parents.
Schools will also have to consider the safety and education of other pupils - and arguments over off-rolling have sometimes accompanied new rules over behaviour.
But off-rolling has also become part of the debate about what happens to pupils who are removed from mainstream schools, including those with special needs, who end up in "alternative provision" of variable quality or who are claimed to be home-schooled.
Why are pupils moving school?
The study from the Education Policy Institute - sponsored by the National Education Union - has examined the movement of pupils between starting secondary school and taking GCSEs in 2017.
The researchers show when other factors are accounted for - such as families moving to another part of the country - there are about 10,000 pupils a year whose moves are described as "unexplained".
These are children, aged between 11 and 16, who have switched to another school, without having moved to another area.
The study does not measure how many of these might be the result of off-rolling, but it suggests this could be an explanation for some of them.
It could also be that families have chosen to move to another local school for other academic or social reasons or personal preferences, with more than three million children in this age group.
The most common time for these moves is in the first three years of secondary school - with fewer moves in the GCSE years.
The study says this pattern is the same as six years before - although the peak, between Years 8 and 9, was slightly higher in 2011.
The suspicion that some schools are removing more pupils than might be expected is from the concentration of almost a quarter of these unexplained moves in 330 secondary schools.
There were similar numbers of girls and boys changing schools, a slightly higher proportion of black pupils and an increased likelihood among those who had been excluded and those in social care.
There was no regional breakdown to show whether this might be more common in big cities such as London, with access to a wider range of schools.
What's the response?
Labour's shadow education secretary, Angela Rayner, said it was a "national scandal that tens of thousands of children are falling off school rolls and potentially out of education altogether".
The National Education Union, which commissioned the report, said it was "shocking if not surprising".
The union's joint general secretary, Mary Bousted, said: "It is urgent that we move beyond the numbers, analyse the real reasons behind these moves and challenge the government policies which are undermining inclusive and high-quality education".
Paul Whiteman, leader of the National Association of Head Teachers, warned "not to conflate and condemn all the different reasons a pupil might leave a school's roll. Every individual circumstance is different".
Geoff Barton, leader of the ASCL head teachers' union, said there was an "uncomfortable reality" that some of these "unexplained exits" could be because of the "illegitimate" behaviour of schools.
But he said it was also important to "keep in mind that many parents make the decision to move or home-school their child for their own reasons".
A Department for Education spokesman said: "No head teacher goes into the job to remove a pupil from school - and no head teacher takes the decision to do so lightly.
"It is against the law to remove pupils on the basis of academic results - any school that does it is breaking the law.
"We have written to all schools to remind them of the rules on exclusions, and Edward Timpson is currently reviewing how schools use them and why some groups of children are more likely to be excluded from school than others."