There's this mature maple near the patio that provides shade but also competes with anything in a 25' radius from its trunk --- including grass. There's actually only a small quadrant that truly suffers from the dense matting of the maple's roots and the shade it creates. I can count the blades of grass in this area of about 10' and 10'. I just scraped the soil, removed what little grass there was and am planning on planting ground ivy which I know will succeed. Anything else that can work in amongst the ivy. Keep in mind, it's shady and I can't dig many holes more than 6" in diameter here and there.