She is the daughter of Paul's cousin

(so she is Paul's second cousin once removed)

@dude,

although 'second cousin' would be incorrect, as it would refer to the daughter of Paul's mother's (or father's) cousin.

you're right. I still find these relations very confusing, probably because I don't have a lot of relatives myself. :-)

It's very simple- everyone in your generation, who isn't a sibling, is a cousin.

Everyone in your parents' or childrens' generation, who isn't a sibling of your parents (i.e. aunts & uncles) or your children, and who isn't your niece or nephew, is a cousin once removed (i.e. the children of your 1st cousins are your 2nd cousins once removed, the children of your second cousins, are your third cousins once removed, etc.)

In German it's even simpler, as everything on the avuncular level remains an aunt or uncle, but "zweiten, dritten, vierten Grades", etc.

There are actually tons of threads about this on LEO: Dictionary: cousin

@Richard
re #1 - so she is Paul's first cousin once removed
re # 5 >(i.e. the children of your 1st cousins are your 2nd cousins once removed, the children of your second cousins, are your third cousins once removed, etc.)

the children of your 1st cousins are your 1st cousins once removed
the children of your 1st cousins are your children's second cousins

and the children of your second cousins are your second cousins once removed, etc.

[edit] and here's a couple of nice simple diagrams:
http://en.wikipedia.org/wiki/File:Cousin_tree.png
http://www.sonic.net/~fredd/cousins.html