I tend to think of "cottonwood" in 2 separate situations; the enormous "river bottom" cottonwood that we get up here and that I have also seen in waterways in every western state we have lived in. They get reasonably tall but they get REALLY big diameters and really branch and spread out and generally look gnarly as hell
Then there is the cottonwood/black poplar that grows in uplands; it is usually the first thing to pop up in disturbed soil, it has shallow lateral roots that spread like a spiderweb and can go for 50' or more with plants shooting up every so often
This stuff grows straight and very tall because it is usually competing with birch and spruce for space and sunlight
And yeah, if you take some down you better do something with it because a year on the ground turns it to junk
We also have a lot of western aspen which is another poplar species