THE formation of nanometre-scale surface structures by atomic manipulation with the scanning tunneling microscope has opened up opportunities for creating new metastable states of matter atom by atom1. The technique allows the fabrication of arbitrary structures, but its application may be limited by considerations of speed, as only one nanostructure can be built at a time. Here we describe the simultaneous formation of many densely packed nanostructures of various morphologies using diffusion-controlled aggregation on surfaces. By exploiting the dependence of the mobility of adsorbed atoms on substrate crystal face and temperature, we are able to grow linear, two-dimensional or tenuous fractal aggregates of nanometre dimensions. The high number density (10(11)-10(14) cm-2) of these structures means that their physical and chemical properties can be easily measured with conventional surface spectroscopies.