How to create a new family tree (not related to my family tree) ?

Piotr, you can do this by following five steps:

1) Add the non-relative as a child of someone in your tree
2) Follow the link to the new profile
3) Edit the information so that it's about the non-relative
4) Cut the relationship from your relative (the temporary "parent")
5) Have fun building their tree!

Does that make sense? I hope I've explained it well enough, but it might be confusion, so let me know.

Ashley. That will work for a Pro or curator.

A non-Pro non-curator like Piotr will hit trouble at step 4 - he won't be allowed to split the tree.

So you need another step

3A) Become Pro or ask a Pro or curator for help.

David, the mechanism is still the same no matter who does it. But yes, you may need someone else to cut the tie for you.

Yes - that's why I added step 3A). Steps 4 and 5 then continue as before. Especially step 5.