Pokeweed, Phytolacca americana I believe.

Here's some info which may help you decide. The sheer size of these huge plants, their large root system, and ability to procreate so prolifically makes them an agricultural nuisance. Unless the previous residents were growing this as a crop, your abundance of sprouts is testament to why this plant is usually not allowed in gardens. Although it is attractive and interesting to look at, red stalks, big soft leaves, dark berries, a native... next year you'll have many more than you would want or have room for. Not only does it spread by seedlings, it is an herbaceous perennial. Through a methodical cooking process, parts of this plant are edible. I've not tried it.

Here is a link that might be useful: Phytolacca at Floridata

Thanks so much everyone. I have begun the process of eradication, and am stunned to see such large roots. Your responses to my original post are much appreciated.