formation of the main deposit. At lower current densities, it is possible to deposit only this extremely thin tin film: it is 5 nm thick (Fig. ), and composed of a carpet of small grains side by side. Whereas the 200-nm copper and 300-nm tin films in Fig. have a thickness close to that predicted by theory, the 5-nm film is much thinner.We expect that the deposition reported here will be possible with any metal that is known to deposit in the powdery regime of growth, in the shape of rounded crystals. We propose the following mechanistic explanation of this effect. First, in thin cells, and with a binary electrolyte, very high fields are generated at the tips of the deposits 17 . These very high fields induce nucleation and growth of a polycrystalline deposit 19 . As it is observed that growth is much more rapid in scratches 5,20 , it is clear that the dangling bonds of glass have catalytic properties, under the action of the large electric field. We now consider why the deposit should be covering for higher currents. As seen in Fig. , this surprising stability is not due to an increase in the size of deposit features up to the sample size, but to a progressive closing of voids between ever-smaller branches, in which individual grains become themselves ever smaller 19 . This proves that, as the growth speed is increased, the capillary length of individual branches is decreased (as expected from theory 9,23 ). But so is the typical size l of gradients ahead of the deposit, because 16, where E 0 is the electric field in the bulk, and z c , z a , m c and m a are the charges and mobilities of the cations and anions. When l becomes smaller than the grain size, instabilities cannot develop, and the front is stable ('absolute stability' in the context of pattern formation). This stability makes it possible to electroplate insulators in conditions very far from equilibrium. The coating of fibres, ribbons and plates seems possible. Many applications of this process may be considered, such as replacing the vapour seeding process in the electronics industry, tailoring mirrors of unusual metals or shapes, and direct coating of organic materials. In general terms, the process proposed here has some advantages over conventional electroless deposition on insulators, in that the film progression and grain size are controlled externally, the process can be interrupted at any time, and it should work with many simple salts, even without additives. But it should be acknowledged that, as the deposition process starts from one end of the sample and progresses towards the other end at speeds of the order of 1 m h 21 at most, the overall production output would be much smaller than existing electroless techniques, which coat in approximately 5 minutes glass plates of size 4 m ยฃ 4 m.We note that using this very rapid plating technique with Li, as reported here for Ag, Cu and Sn, might eliminate the cycling problems of Li rechargeable batteries. Indeed, cycling efficiency of Li batteries is drastically reduced by dendritic growth. This is ascribed, in part, to the poor cyclability of a powdery tree. In present designs, dendrites are always seen to grow perpendicularly to the electrodes. A set-up similar to ours would in principle generate a thin film whose morphology is easier to cycle.A