One way to think of it is through the good ol' evolutionary framework. It's possible (I'd even dare to say probable, acknowledging my complete lack of study in the subject) that there were many abiogenesis occurances on the early earth. Perhaps the first few were wiped out by a new asteroid impact, and more had to start. Maybe some that started were in a pool of water that evaporated and they dried out and died. Ultimately, only a few trees would get started enough to really be able to adapt, or be in stable enough environments that they didn't have as much anti-life forces working on them.
From there, it comes down to competition. At furst, each tree could grow as it pleased. Some probably died out, maybe some new ones sprouted, but eventually, they would come into conflict with each other. Competition for resources, predation, even on the microscopic level, would tend to favor the more adaptible trees.
Ultimately, one tree dominated over the others, and resulted in all the life we see today. It's possible there are a few scraggly trees hanging out on the fringes, clinging tenaciously to life under the shade of the massive tree we belong to. It's also possible that there are known organisms that aren't part of our tree and we just don't recognize it. Are viruses maybe a holdover from another tree that has adapted itself to us? One problem would be that any coadaptation between trees would entangle them to such a degree that sorting out if any particular branch is from one tree or from another one may be difficult, and since we can't necessarily follow the branch back to the trunk because of the limitations of the fossil record, especially with respect to single-celled, or microscopic multi-celled life, we may never know.