Declaring someone an illegal immigrant doesn't necessarily make him go somewhere else. Especially if he is from some country where employment is even harder to find. Less so if we're talking about well-educated or at least skilled immigrants. They tend to go where they are more wanted.

The small, rich countries in the north have a lot less problems with controlling immigration, owing to cold or wet borders, low absolute population and low population density. These countries only recently became attractive to immigrants. They may even be able to deport most of the illegal immigrants.

Germany for example can't expulse illegal immigrants on a grant scale. Justified public outrage about "German mass deportations" would even be the least of problems. It's just logistically and politically impossible.

That's why I say that immigration is almost impossible to regulate effectively with the means available to a democratic nation. You'd need some kind of STASI to hunt down hundreds of thousands of immigrants. Nothing would be worth that....