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Cohan,It does look araceae, doesn't it. I've never seen an aroid with runners quite like that though, unless you're thinking along the lines of Philodendrons etc. I wouldn't expect them to live outside for years in Mark's conditions though?Actually, having just checked Mark's original comments, my assumption of long term (i.e overwintering) is incorrect, which definitely does open up quite a few other possibilities such as Philodendron etc. A flower would of course sort out a lot.
chlorophytum was my first thought too, though i don't know species with leaves like that (not that i know anything about various chloro species!)