A 5 gallon bucket is sufficient for a 4x4 plant, 5x4 whatever. I know a guy who grew plants up to 6'Hx5'W in 5 gallon buckets and they where very healthy still in late summer. (last I saw em)
you could probably mix up some good organic soil and use the 10 gallon pots. It wouldn't hurt but I think it's overkill unless it's all summer in a greenhouse. I think as long as you don't over-water, the nutes would be fine (not flushed out) if you started with A++ soil to begin with.
As far as the actual question you posed. Factors regulating root growth would be genetics, availability of nutrients, moisture and oxygen and of course available space.
The primary root mass of a mammoth 6'Hx8'W wide plant I grew one time was maybe 18"x24"x10" deep, it of course had some axillary roots but I was surprised how small it actually was.
I veg to 36" tall in 5 gallon pots no problem I go quart, gallon, 2.5gallon, 5 gallon tweaking my soil each time I re-pot. I transplant each time I see growth slow down. I works well and I believe it maximizes root development.
The theory goes like this, you force the plant to make the most of it's available space and then replant it. The plant will be all stoked that it has new soil to exploit and quickly expand it's root boundaries to utilize the new nutrient rich soil, creating a larger and larger root mass. If you plant directly into the largest pot, some say, the plant will quickly expand to it's maximum boundary without maximizing it's root mass to take full advantage of the available area. essentially skipping over valuable nutrition.
Now one could argue a plant is smarter than that and will selectively mine out the nutrients it needs from the whole of the available soil. One could also argue that the "maximized" root mass would in the name of efficiency discontinue usage of any portion of that root mass that no longer provides enough nutrients to justify it's existence (there is some natural law about that). Personally, I believe the large pot first theory would greatly reduce the potential for stress, allowing the plant to do it's own thing more naturally. However a certain amount of stress supposedly reminds the marijuana plant it needs to defend itself by producing copious amounts of cannabinoid. So it all really boils down to a personal decision. Maybe you could do an experiment trying each method with identical clones and post the results, that would be kinda cool.
