Takes over my yard edges, fast growing, no vine. Individual stems (from ground) with 3 leaves. Does not flower, no berries, nothing but green leaves. Stems are also green and weak. I pull handfulls and they easily snap off at base, but root stays underground.
I am sorry, but we have not been able to identify this plant. Several Extension staff here on eXtension have been baffled, as have I; I shared this picture with Purdue University staff and several of my Master Gardener volunteers, and nobody knows what it is.
It sounds like you are most concerned about controlling this plant, whatever it is. That I can help you with!
I would recommend using an herbicide containing glyphosate (Roundup). This should be mixed and applied according to label directions. I have had better luck with permanent elimination of weeds by spraying a light misting of Roundup on the plants then by trying to drown them with it. The chemical needs to be absorbed through the leaves and carried down to the roots. If you mix the spray too strong, or drench the plants too heavily, you will burn the leaves off before enough chemical has been absorbed to kill the roots, and the plant will regrow. A light misting may not completely kill the plants, but you can always make a second treatment about 2 or 3 weeks later.
Be careful not to spray any Roundup on the lawn or desirable ornamentals. However, depending on how thick this infestation is, you may need to sacrifice the grass in this area to get rid of this plant.
Please contact me directly (email below) if you have any other questions.