Far better to leave them as one unless you like doing double entry.
Which tree will you put you children in, or you grandchildren?
What happens when you find one of his ancestors married one of your ancestors (and yes- sooner or later you *will* find such a case)?
Which trees get the pictures?
For these and many other reason most dedicated genealogists recommend having only one tree; you can, of course, work on any section at any time which makes it easy to maintain.
If you must have more than one you can't split them online. You must download a GEDCOM of your online tree, use your genealogy program to split off the part you want, create a GEDCOM of that part and unload that GEDCOM to begin s new tree.