I've googled Existence, and found this article on Wikipedia:http://en.wikipedia.org/wiki/Existence#Existence_in_the_wide_and_narrow_senses
However, it did not answer my question.
Some star some far away from our galaxy that does not influence our lives at all, or at any point, and which we might not know wether to exist or not, does it exist anyway?
Of course it does. Even though it does not affects us in any way what so ever, the star exists regardless of wether we believe in its existence or not. Einstein expressed it as:
"The moon exists no matter if I look at it or not" (now, this is a poor example, because the moon does affect our life, ie, Tides, causing the sealevel to rise and fall.
However, even if the moon did not affect anything on the planet Earth, I'd still say it exists.
Something does not have to exist in relation to something else, in order to exist, which is what many people tend to believe in these days of "relativity-thinking".
There IS an absolute Truth, we don't know what it is, but it is still there.