Vireya thought that the self sown tree that appeared in my garden might have been a Melia azedarach a rather pretty rainforest tree. It is a deciduous native tree also found in Asia. I have one of these and so when I found another little Desert Ash growing in the garden I was able to do a direct comparison.
Here are the leaves of the two plants close together, very similar indeed. But already it is obvious the Melia azedarach leaves on the lower right are slightly glossy and the serrations on the edges are rounder.
Another difference is the way the leaves grow out from the leaf stem. Those of the Melia azedarach branch out on opposite sides down the whole length. Then that stem has a quite long bare part before it joins to the branch. The leaf stems of the Desert Ash are opposite each other, but each pair is rotated a quarter turn on the stem from the previous pair, so it will not lie flat as you can see in the photo.
Melia comes from the Greek for Ash Tree because the leaves are so alike.