Let it get large enough so the stem can soak in a lot of glyphosate. (Don't let it go to seed of course.) ... Snip it off and paint the stub with undiluted G.
I believe the little ones - come from the roots of the big one.
Water/air ratio in relation to water flow to/from any plantlife is a Basic Fundamental Concept in understanding seed germination as much as transplanting a 20' Maple tree in 90 degree weather...