Escoffier On Line

at what point does starch thicken in vegetables with root bases

Depends on the root.

Here is some general stuff from Wikipedia
"Many thickening agents require extra care in cooking. Some starches lose their thickening quality when cooked for too long or at too high a temperature; on the other hand, cooking starches too short or not hot enough might lead to an unpleasant starchy taste or cause water to seep out of the finished product after cooling. Also, higher viscosity causes foods to burn more easily during cooking. As an alternative to adding more thickener, recipes may call for reduction of the food's water content by lengthy simmering. When cooking, it is generally better to add thickener cautiously; if over-thickened, more water may be added but loss of flavour and texture may result."