Apart from excluding light from developing tubers the main purpose of earthing up is to excourage the formation of rhyzomes (runners) from the leaf axyls. Earthing up before the leaf axyls are developed simply results in etiolation of the stem - so much wasted time and effort from the plant`s point of view. However, earthing up over a developed leaf axyl will result in the production of a rhyzome. If the plant is nearing the stage when tuber initiation is provoked the rhyzome will start to form a tuber; if the plant has not reached this stage the rhyzome will develop into another shoot which will produce hair-like roots of its own (these roots are not the same as the ones which initially form at the start of the plant`s growth - a potato plant makes 7 different types of roots in its development), but when the plant reaches the stage of tuber initiation these shoots will themselves produce more tubers. The more leaf axyls that can be earthed over, and the more rhyzomes that develop the greater will be the crop.
The ideal is to allow each leaf to develop on the main stem and then to earth over the joint - it doesn`t matter if the leaf also gets covered because there should be at least 5 or 6 inches of growth above and the plant will continue to make more top growth until it is mature. This will result in the greatest crop from a small space.
However, holding the leaves up against the stem (as Aquilegia suggests) simply defeats the object of the exercise - as the leaf axyl is not in contact with the soil the shoot which develops will simple be another side shoot which, although it increases the `top hamper`of the plant, will not be a rhyzome.