ToE claims a single tree, and creationists claim multiple small trees.
quote:
There is grandeur in this view of life, with its several powers, having been originally breathed by the Creator into a few forms or into one;
From Darwin page 459 "Origin of Species".
Aside from the above which is really neither here nor there, the ToE doesn't suggest on it's own that there is one or multiple trees.
What we find when examining life is that the evidence says there is only one major tree with extant forms today (that we recognize anyway). This isn't part of the theory it is a consequence of applying the theory to the evidence we have at hand.
All of which may only be saying what you have already said in your post. However, the pedantic nit is that it is not a consequence of the theory but simple what we observe in life here today.