The growth of banded hedrites of isotactic polystyrene (iPS) is followed in situ, using atomic force microscopy (AFM). The melt layer surrounding the growing hedritic front is much thinner than both the hedrite front and the far-field melt. Growth occurs simultaneously in three dimensions: radially, eircurnferentially and height. The height of the hedrite growth front being so much higher than the adjacent molten pool, the observed propagation of the front requires that it be covered by a thin film of molten material, likely drawn up the face of the front by capillarity. As the hedritic front grows in height, it demands material at a higher rate than can be delivered from the far-field melt and the stacked lamellae stop growing, layer by layer, from the top downward, until only the basal lamella continues to grow (at a constant velocity). The kinetics of the position of the lowest point ahead of the growth front slows with time during this process. Supplying only the basal layer, the adjacent molten pool is replenished and now begins to feed new layers of growing lamellae as the process repeats itself. The creation of the new lamellar layers appears to be coupled to morphological instability of the basal layer, in the form of growth front serrations, likely causal of the giant screw dislocations. (c) 2005 Elsevier Ltd. All rights reserved.