Identification: Grandmother's legacy, 25 yr. old mystery plant

My Nan brought back seeds from a trip to Spain/Portugal from a native species in 1980. This plant grew in her house until I inherited it and no one who has seen it has ever identified it. It stands now at about 3' with a woody base and fleshy stem. The leaves grow in the shape of an umbrella and it likes lots of sun (eastern exp.) It regularily sheds the lowest leaves and as they yellow and fall off and a milky substance seeps from the site. It also seems to be constantly flowering from the stem. Buds develop, 2mm in size as a cluster. Tiny, white petals protrude from the buds. Next, the buds dry, open and scatter small black seeds which self sow. Most of my family now has a plant from these seeds. Please help me identify this plant and solve a family mystery. I have attached 2 photos for viewing. Thank you.

 

You'll find your answer in this thread: Identification: - ID help!!! | UBC Botanical Garden Forums.

 

Thank you so much for the info. Family mystery succesfully put to rest. I wonder how old these plants can get as mine is 25 years old and still growing strong. Any thoughts???

 

Sorry, can't help you there. Google's your best bet.