A study by the European Commission shows that only 1% of the working population of the 10 countries set to join the European Union would be likely to migrate to existing EU states, even if they enjoyed full freedom of movement.
That would mean some 220,000 migrants every year for the first five years after expansion.
But the study, based on polls done in 2002, highlights the risk that the EU newcomers may lose young well-educated people.
The loss of skilled young people could hit new EU members hard
The study, conducted for the European Commission by the Dublin-based EU Foundation for the Improvement in Living and Working Conditions, relies on data collected two years ago, when it was unclear how many EU governments would impose labour restrictions on the new member states.
In the event, all of them, except Ireland, have decided to do so, fearing a huge inflow of migrants who would be a drain on their welfare systems.
Romano Prodi, the president of the European Commission, criticised that trend. So, whether by design or not, the results of the study come at a politically convenient moment for him.
"I already expressed my really deep worry, because this not a generous attitude, this is not the spirit in which I work," he said.
"I don't think that the number of potential immigrants will be so huge.
"Our analysis is that it's going to concern skilled people rather than lower-skilled people and so I'm really hopeful that reality will demonstrate that the problem can be solved in a short time."
The study shows that those who declared a firm intention to migrate are only around 1% of the working-age population of all 10 acceding states and the three candidate countries - Romania, Bulgaria and Turkey.
Workers with firm migration plans
Romania - 2%
Bulgaria - 2%
Poland - 1%
Other EU newcomers - under 1%
Turkey - 0.6%
Source: European Commission
That would mean over one million people within the next five years.
That figure could increase fourfold if all those who show some intention of migrating did so, although the study's authors believe that prospect is unrealistic.
The polls were conducted in April 2002 on samples of 500 people in Cyprus and Malta, 1,000 people in most other countries, and 2,000 in the biggest countries, Poland and Turkey.
The study does not show which existing EU countries would be the migrants' favoured destinations.
What it does show are big differences among candidate countries.
The biggest migration potential - 2% with a firm intention to migrate - was found in Romania and Bulgaria, the two countries set to join the EU in 2007.
In Poland, it was 1%, while in the other countries set to join the EU in May, it was below 1% . That is a similar figure to the one recorded in Turkey, where only 0.6 % of working age people said they wanted to move to Europe.
The other important conclusion of the study is the potential migration of young people and of well-educated ones from the new member states.
"Far from a wave of immigration that puts a burden on the current member states' welfare system, the problem that free movement of workers is going to cause is a brain drain and a youth drain in the accession countries," says European Commission spokeswoman Antonia Mochan.
"So the highly skilled, highly qualified people in those countries will be likely to migrate, and that will have a detrimental effect on the economic development of those countries and therefore on their ability to reach similar levels of GDP as the current member states."
There are already fears that Polish and other central European doctors and nurses could be attracted by much higher wages in western Europe, depleting their national health systems of much-needed skills.
The study shows that the typical migrant from central Europe is a young, single graduate or student, often a woman.
The new member states risk losing up to 5% of their young and graduate population, and up to 10% of their students.
In Bulgaria and Romania, the study shows that up to 10% of young people are thinking of leaving the country.
Women are more likely to emigrate in the Czech Republic, Hungary and Slovakia - as compared to men in Bulgaria, Poland and Turkey. Unemployment is less of an influence on migration than believed.
The figures set out in the study are in line with the experience of previous enlargements.
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