I dont have a lot of dirt space to put a tree in the ground to thicken it up. Is there a formula or something i can use for using grow boxes or nursery pots, like is it better to go more wide than deep or vice versa?
For depth, I just use the standard size lumber, a 1x 4 is 3.5 inches, 1x6 is 5.5 inches, you can vary this by putting the bottom boards inside the box or on the surface.
If they are big training boxes a little ear on opposite sides make lifting easy..good luck
I agree depending on the stage your tree is in. I also prefer shallower pots when ever possible. With a limited space, this may not be your best choice though due to bigger foot print.
The way I see it, you need the proper volume for your tree's stage. You can get that whether the container is deep or shallow. The problem with deep container (downward roots) can be remedied by using the tile method.
Also note that the bigger the footprint of your container (shallow container), the more water it will retain vs a similar volume deep pot. Knowing this, you can use it to your advantage and avoid potential water related problems.
It can be elaborate or just do what most nurseries do (the simple way) and up size the pot slowly over the years until you reach the trunk size you want.
As usual, there is no one size fits all answer so learn and apply what best fits your needs.
Water retention isn't only decided by depth, a wider ratio pot hold moisture the best. contrary to what it looks like would happen. My thinnest pot used stays wet the longest of most all my potted trees. Easy to tell too, it's got an apple in it and if it dries it gets droopy, usually in good shape at the end of the day, where deeper pots are dried down more.