Should EU citizens consider becoming British?
These are anxious times for the 2.9 million citizens of other EU countries currently living in the UK.
Not to mention the estimated 1.2 million British expats who live in the rest of the EU.
The free movement rights which allowed EU citizens to set up home here and take jobs (there are just over 2 million EU citizens in the UK workforce, according to the latest ONS figures) could be scrapped if Britain votes to leave on 23 June.
Nobody - not even the most ardent Brexiteer - is talking about mass deportations. The Leave campaign has repeatedly assured EU citizens that their right to live and work in the UK will not be affected if Britain votes to leave. There are longstanding conventions protecting the rights of citizens acquired under international treaties.
It might be a different story for new arrivals, depending on the kind of deal a post-Brexit government eventually strikes with the EU.
But EU citizens are not taking any chances, it seems. Many are reported to be applying for British citizenship ahead of a possible Brexit vote next week, in the hope that it will protect them from being deported if the rules change in the future.
EU citizens qualify for permanent residence in the UK after five years of living there as a worker, partner or family member of a worker, a student, someone who is "economically self-sufficient", or is a "credible" job seeker. They can then apply for full British citizenship.
Immigration lawyers, who rarely hear from EU nationals in normal times, are reporting a big increase in applications that has yet to be picked up in the official figures - which are next expected in May 2017.
"We have had an unprecedented volume of applications for permanent residence," says Oshin Shahiean, of OTS solicitors.
His clients are deeply worried about what might happen to them: "If we do exit the EU what is their immigration status going to be? There is no certainty. The government hasn't put anyone's mind at ease."
The applicants, he says, come from a range of different countries, including many Brazilians who have dual Portuguese citizenship.
All are anxious to become British citizens before next Thursday's vote - but that is not a realistic goal, says Mr Shahiean and the other lawyers we spoke to. Even if they had applied when the referendum date was announced the process is currently taking at least six months.
"Everyone is desperate to become British before it is too late," says Jonathan Hendry, an immigration lawyer with Matini Monte Cristo.
Given all the assurances from the Leave campaign, should they be worried?
Mr Hendry says he would not be concerned "knowing what I know" about the way the immigration system works and the fact that "the government can not ask everyone to leave".
But, he adds, he would be concerned if he was an ordinary member of the public "because there are conflicting statements about what might happen".
There has also been a big increase in the number of British-born people applying for Irish passports on the basis of their ancestry, according to figures obtained by The Guardian from Ireland's department of foreign affairs.
Ireland offers automatic citizenship to anyone with an Irish parent, regardless of where they were born. The grandchildren and great-grandchildren of Irish citizens are also eligible in some circumstances.
Applicants do not have to state the reason for wanting dual British/Irish citizenship but one reason might be a desire to continue taking advantage of free movement rights if Britain leaves the EU.
The legal experts we spoke to suggested some Britons with foreign-born partners were rushing to take advantage of a loophole, known as the Surinder Singh route (after a court case which established it), before it closes.
Under UK immigration law, British citizens who wish to bring a non-EU partner to the UK to live must earn more than £18,600 a year.
They can get round this by moving to another EU state, normally Ireland, for a minimum of three months, have their partner join them and then move to the UK together under free movement laws, without meeting the UK earning requirement.
The Surinder Singh route could be shut down as a result of measures in David Cameron's renegotiation of Britain's EU membership.
Former Indian and Pakistan nationals have made up by the far the biggest group of new British citizens in recent years. They totalled 31,489, or 25%, of total grants for the year to March 2016, the most recent Home Office figures show.
Grants of British citizenship to EU nationals made up 11% of total grants in 2015. This has increased from 4% in 2011, mainly due to an increase in grants to Poles and Romanians.
Some 850,000 Poles are living in the UK but only 3,764 of them were granted citizenship in 2015, an increase of 597 on the previous year. It was a similar story for other countries with high levels of migration to the UK.
But there is anecdotal evidence, from immigration lawyers, of a big increase in applications for citizenship in the past few months - the next official figures will be published in May 2017.
(The rules for EU citizens applying for British citizenship were tightened up in November last year - they now have to have to apply first for a permanent residence certificate or card, which involves filling out an 85 page form and paying a £65 fee.)
The majority of EU citizens in the UK don't bother to apply for citizenship, even if they have been in the country for decades and have children or partners who are British citizens because, under current free movement rules, they don't need to.
Applying for citizenship can be an expensive and time-consuming business.
And many people like to remain citizens of their home country while working in the UK for emotional and family reasons.
The same reasons that most British expats living in the EU - including the estimated 100,000 who have retired to Spain - remain British citizens, although there are reports that some are seeking dual citizenship over fears of what might happen to their immigration status if Britain votes to leave.
EU citizens living in the UK
Carla Herbertson, from the Netherlands, said: "I came here as an au-pair when I was 17 and then returned after university to work as a journalist. I married an Englishman and have two children who are six and three. They are both British citizens but I'm still Dutch.
"I'm so against leaving Europe out of principle. I was able to come and work and establish myself in Britain. I've lived here for 18 years, I pay taxes and am an active part of society. I was even called for jury duty, so I'm really frustrated that I can't vote.
"However, I won't go for British citizenship. Even though I feel part of British society and I love living here, being Dutch is part of my identity. I shouldn't have to give that up."
Vote Leave insists neither group has anything to worry about.
"I could see why, as a citizen of another EU country, you could have some concerns but I think there has been some irresponsible whipping up of those fears by the other side," a spokesman said.
"It does not matter how long you have been in the UK," he explains, everyone will be given "indefinite leave to remain".
"The same goes for British expats in Spain and elsewhere, who are not going to be airlifted back to the UK," he adds.
"We are not here to deport people or send people back. This is about establishing control in the future."
The problem with Vote Leave's assurances, says lawyer Colin Yeo, of Garden Court chambers, is that they are not a "government-in-waiting" - they cannot guarantee anything.
His point is echoed by Britain Stronger In Europe's chief campaign spokesman, James McGrory, who says: "On the status of EU citizens living in Britain, as on so much else, the Leave campaign just don't know what would happen if we leave."
Vote Leave wants the government to introduce a "points based" immigration system for EU migrants, which would bar entry to unskilled workers, a process their spokesman said "could take a few years".
The finer points of the policy, such as what rules would apply to very recent arrivals, including people entering the country after the date of the referendum, would have to be decided by the government.
In the circumstances, it is not hard to see why people concerned about their future status would want to seek the insurance policy of becoming a naturalised citizen of the country where they have set up home.
Most legal analysts say those who already have permanent residence status will be able to keep it, or continue to seek it, provided they remain in employment (unemployed people will almost certainly become easier to remove if we leave the EU).
But we are in uncharted waters here. The courts could be kept busy while any new system beds in.