Take for instance the name 'Kowalski' which means 'from the smith'. Considering the number of smiths there were in the Middle Ages and later, I think the answer is clear that somebody in the center of the country could have been called 'Kowalski' as somebody near the borders could have been called 'Kowalski'.
That's the same as asking if people with the name 'Swiatopelk-Czetwertynski' (a Belgian princely family with Polish roots) are all related. Well, because there are so few people with this name, it's very likely they are related.
I think it's reasonable to assume that the larger the number of people with the same surname is, the smaller the chance is they are all related.
If anyone in PL had a relative (probably from the wartime generation) who went to Leeds in the UK or the area around Leeds with one of the following surnames, there may be some money waiting for them. This is from the UK Treasury list of unclaimed estates, where someone has died without making a last will and testament and no relatives have come forward in the UK to claim the deceased's estate.
I've just included the Leeds surnames (without Polish characters). The full list (for all the UK) can be found in the link which also explains how to make a claim.
