Hello rjbcrest,
Welcome to the board. I hope you'll stick around.

That's the way those babies grow, so to speak :) We call them "suckers" and what you're doing is the thing that we all do.

When you repot the plant/suckers, perhaps you could look for the source of those new suckers/plants and break it away.

If you're wanting a way to prevent suckers from ever returning or appearing, you are in for a long and dead end haul.

Many of us just break them off (with a sucker plucker or something) and some even try to start new plants from those suckers.

Dora