Is there any relation to the size of the root with size of the plant? In other words can a small plant have nice roots and vise versa ?

Oh yes. Ive dug medium size roots with huge 4 prong tops and large roots with small 3 prong tops.

I may be wrong but i think it has to do with soil condition. Ex: dryer soil equals bigger root to reach mositure

Their are times that a smaller 3 prong will have a decent sized root but in my experence the real big plants mostly have the bigger roots.