They reproduce either asexually, although you might go blind, or sexually.
The spores can settle (often on gravel) and form tuffs and eventually form new balls after a few months. All balls are hairy unless you trim them.
Ball splitting is the best way to divide after they get a decent size and start becoming uncomfertable (for the tank) and taking up too much room. Some balls, when happy, will float up to the top of the tank from pearling. Great balls are always pearling and bob up and down daily.
Regards,
Tom Barr