An earlier paper, describing observations at a wavelength of 3 cm with the Australia Telescope Compact Array between 1992 June and 1994 May, showed the supermassive star eta Carinae to be in the threes of a major outburst. This paper, based on observations at wavelengths of both 3 and 6 cm, describes the evolution of the outburst since 1994 Map. From 1994 May to 1995 December, eta Carinae's image continued to expand, and its total flux density to increase. These dramatic changes were caused, we believe, by an outburst of UV luminosity, and consequent ionization of pre-existing circumstellar gas clouds. Since 1995 December, eta Carinae's total flux density has fallen. The large-scale structure of the radio image closely resembles Ha optical images of the eta Carinae 'Homunculus' nebula. Tn addition, the central area shows fine-scale structure, principally comprising a secondary source about 1.2 arcsec to the northwest of the star, which we believe to be a dense gas cloud, and a ridge of length 4 arcsec centred on the optical position of the star, which we believe to be an equatorial disc or torus. These structures are seen also in 3-cm (H91 alpha) recombination-line emission.