as in totally remove? Cut the stems down to about 2" tall and apply SBK weedkiller to the stumps.

if you mean the invasive bits then trace them back to the base and cut off as close to the main stem as possible.

Welcome to GoY too

Are you sure the runners are from the Fatsia ? Ive never seen then put out runners in 32 years of profesional gardening

Have had a Fatsia for 15 years and never seen it put out runners either!

Just a way out idea - could the runners actually be Acanthus mollis? Admittedly leaves are a different shape but they are big and shiny and it spreads like wildfire.
Sorry if its a stupid suggestion.

Photo of plant and runners would be very helpful

I'm with Badfish - they don't put out runners. What does happen from time to time is they seed themselves and you find new plants growing nearby, and you may not have noticed them as they started growing. If they are separate plants, as is likely, you can just dig them up.

Fatsia do not produce runners. I have almost every variety and species and I can tell you they do not produce runners! I can only think that they have self seeded or you do not have Fatsia, so I echo the above and shoe us a pic.