"I think that in the vast, vast majority of countries (all of them?), you receive the citizenship of your parents, regardless of the country in which you're born."
For the UK at least, it's not that simple, unless your parents were born in the UK. If your parents citizenship is due solely to one/both of your grandparents being UK citizens (i.e. your parents were also born overseas), you might not be entitled to UK citizenship.
I don't recall the details, but IIRC you need to live in the UK for some time in order to pass on citizenship to your child.
For the UK at least, it's not that simple, unless your parents were born in the UK. If your parents citizenship is due solely to one/both of your grandparents being UK citizens (i.e. your parents were also born overseas), you might not be entitled to UK citizenship.
I don't recall the details, but IIRC you need to live in the UK for some time in order to pass on citizenship to your child.
The US has similar rules.