The plant in the attatched picture is slowly taking over my garden. I dont know what it is, and it seems to choke out the plants I want to keep. Any ideas of how I can control it? Right now, we slice off the top 1/4 ” of soil and dispose it but that doesnt seem to be doing much.
Although your image is a tad out of focus, hence difficult to clearly see the plant’s leaf pattern, I see a few other elements in the picture. There are maple tree ‘keys’ on the ground, some wild clover growing, and a few pieces of trailing growth that could be root sections, all surrounded by moist, and otherwise bare soil. So perhaps this area is under, or adjacent to, a maple tree, which, when in full leaf, would cast medium to dense shadow. And perhaps your mystery plant propagates with sub-surface runners, in which case, even small sections of roots left behind (after your surface removal) could easily, and with surprising speed, regenerate.
So while your plant does not appear to be one of the usual surface-dwelling suspects, such as chickweed or knot weed, it is thriving in semi-sunshine, and opportunistically growing where other plants perhaps cannot. As a guess only, and because of the starburst-shaped plant tops, this could be Winter aconite that has now gone to seed. Eranthis hyemalis (family Ranunculaceae) is a combo tuber-rooted herbaceous perennial that will spread readily. Did this plant have butter-cup like blossoms in the very early spring? Another possibility would be one of many varieties of starwort, a moisture-loving, creeping plant. Either way, you have asked how you can control this plant, but not eradicate it all together. Your best plan might be to plant other ‘some-sun-to-shade-loving’ perennial species, and once they are established, the hope would be that this ground-hugging plant might encroach less. Research astilbe, ferns, heuchera, hosta or hydrangea and visit a few nurseries, to see first hand varieties that both appeal to you, and would thrive well in this location. For an absolute plant ID, you are welcome to send a few close-up, detailed images, both leaves and blossoms, if possible, as a follow-up.
To assist with your research, please see this Toronto Master Gardener article that contains several related gardening Guides and a link showing Ontario weeds to help identify your weed: http://www.omafra.gov.on.ca/english/crops/facts/ontweeds/weedgal1.htm#ten