Answer: In general, these trees have very few pest problems, and if ever something should begin to happen then your best approach would be to take a sample to your county extension and have them identify it and suggest how to control it. In any case you need to identify a pest first, then determine the best way to control it.
If the growth along the trunk consists of small leaves and soft stems you can simply rub them off with your fingers. If slightly larger, use a sharp bypass pruner to remove them. Leave the collar or slight swelling at the base of the stem intact because this is what will heal over the wound. You could do this type of tidying up now. Any dead or damaged branches can also be tidied up at any time.
If you want to remove larger branches from the base, keep in mind that to some extent the tree's branching works to shade its own roots thus helping to keep the soil moist and cool the way it prefers it to be.
Some of these trese are grown as muiltistemmed specimens, some as a single trunked tree. You will want to consider the overall long term shape of the tree when you remove branches of any size. Without seeing the tree it is difficult to picture the effect you wish to achieve, however I would strongly suggest you look at a book or two about fine pruning for ornamental trees before tackling too big of a job or making any drastic changes to the tree. If nothing else, most varieties of this tree grow relatively slowly so you want to be judicious in your cutting. Always stand back often to check the results of your work.
The tree will adapt well to pruning, however never remove more than a quarter of the canopy at a time, meaning in a season. You might also want to wait until next year when the plant has become established before you prune as pruning can stimulate excess growth and cause additional stress on the new root system.
Enjoy your tree!
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