There are two extremely fast-growing trees in my neighbor's yard that have pushed through my fence, which in the Philly code means I can now prune them without asking. The problem is I am not sure what they are, or even if they were planted on purpose. (All of my neighbor's landscaping decisions are made by an older relative who lives in another part of town and is extremely stern--he comes over, does stuff, and leaves, and no one dares ask him what he is doing.) The best match I could find on Leafsnap was black willow, but we're in an urban neighborhood, not near water. It very much looks like the trash trees that grow in abandoned lots, although the flowers are pretty.

If it is a black willow, and I want to prune my side, can I prune it into a tree shape (rather than gigantic shrub, which is what it looks like now)? Are there other species it might be?