Neoblasts make up a substantial fraction of the worm's cells and are distributed through the body. They are the sole source of new cells in adult tissue, and at least some are pluripotent: single-cell transplantation experiments have shown that one neoblast can restore an entire lethally irradiated animal and repopulate all its tissues.
Rebuilding also requires knowing what is missing. Wnt signalling along the body axis sets head-versus-tail identity, and interfering with it produces the striking result of a two-headed worm regenerating from a trunk fragment. Similar positional signalling controls the medial-lateral and dorsal-ventral axes.
There are limits worth stating plainly. A fragment must contain neoblasts and enough tissue to organise, so very small pieces fail, and figures for the minimum vary with species and technique. Separately, the mid-twentieth-century claim that memory transfers when trained planarians are fed to untrained ones is not accepted; those experiments were poorly controlled and the underlying question of what planarian regeneration does to memory remains genuinely open.