Ah…the Brazilian Pepper. Birds eat the berries and get drunk, and poop all over everything.
Back in the late 60's my dad planted a hedgerow of Brazilian Peppers all the way around the back yard. Must have been 30 or 40 of them. They grew so rapidly that he was forever out there in under the blistering summer sun trimming them. The sap is sticky and caustic. After their trunks got to be about 8 inches in diameter he undertook the gargantuan task of digging them all up and replanting the hedgerow with podocarpus.
Nasty plants they are. And one of the most destructive of native plant life.
Be merciless in eradicating them.
I'll be merciless, but I think we're in a losing battle with the birds pooping the seeds all around.