The country needs to have no VPs. Even if they have one little VP province all the way over in China it is enough for them to avoid being annexed (I'm looking at you Portugal). But it doesn't matter who controls those VPs. Whoever owns the Capital will get the option to annex when the VPs drop to zero.
Probably worth point out that capital means the province that was capital when that nation held all its provinces (e.g. for Germany that is Berlin; although if you take Berlin it will move to another province, if one is available, but just holding Berlin is enough to satisfy the Capital requirement).