brisbane box tree

Thinking about putting this tree in our front yard. I am wondering about the root system. Does it have the problems associated with a shallow system or is it invasive? Would a root barrier be recommended?

Tristania confreta can get to be a fairly good sized tree, if you let it. In this case if you keep the tree trimmed back some, the root system will probably not get as large because it is not supporting a huge tree. They can grow to 50 or 60 feet if everything is to their liking. But you can keep the tree to 25 or 30 feet with some annual pruinng, (maybe even less if it is done right from the beginning) perhaps every other year might do.
Some depends on what is in the area also. If there is a lawn or other 'water source' the tree will grow faster. Same if it gets a lot of fertilzer. If it is in an area that you can withhold water so it is not always moist, that will slow the growth too.
Genearlly the roots of Tristaina are not considered to be a problem. However some depends on the soil it is planted in, and how the tree is watered over a long period. If the water is applied deeply and less often it encouages deeper root systems. But if the soil is like concrete and there is 'no where to go' the tree will take the course of least resistance and where the moisture is, near the top.
So if you have half way decent soil and get it off to a good start with deep waterings, keep the tree trimmed so it does not become too large, it should be a nice tree with few problems.
FYI there is another Tristania that is 'naturally smaller' growing. It also does very will in our area. It is not as well known for some reason, but it is just as nice, in my opinion. It does have smaller leaves, about 2/3 smaller and the tree blooms with a light yellow bloom. You can 'google' Tritania laurina. Because it is smaller, it will take a little longer to get to say 15' tall, quite a bit longer but it is another option you might consider, unless you want something in the 25' - 30' range this one will not work.