Researchers at the London School of Economics and University College London have studied the effect on crime of two large migration flows to Britain. One was the arrival of large numbers of economic migrants from eastern Europe after the enlargement of the EU in 2004. Rates of violent crime in the parts of England and Wales where they settled remained stable and property crime fell...Economic migrants are likely to arrange jobs before they arrive. Few are unemployed. Studies in America have shown similar trends: the crime rate among first-generation immigrants is lower than the overall crime rate.
The second group were asylum seekers...their presence had no impact on the prevalence of violent crime. Property crime did, however, rise slightly. Part of the reason behind this is the contrasting circumstances of asylum seekers...Few planned to leave their homelands.The funny part is that their native born children commit crimes at the same rate as the rest of the native born. Sounds to me like they'll be as American or British as anyone else.
On the emigration side, I found this:
Ireland's situation is still perilous...Only mass emigration over the last five years has stopped its unemployment figures from rising...Emigration now even seems to have formally become a government policy to reduce unemployment figures.But that shouldn't be too surprising. Ireland has used emigration as a safety valve for centuries, why change what works? Fun fact: Ireland's population before the Great Famine was over 6 million people. Many emigrated because of the famine, but the trend continued until the mid 20th century, when the population bottomed out just under 3 million. Today Ireland's population is still below its peak, at around 5 million people.