We derive the outage capacity regions of fading broadcast channels for code-division (CD), time-division (TD) and frequency-division (FD), assuming that both the transmitter and the receivers have perfect channel side information. The zero-outage capacity regions and the associate optimal resource allocation policies are obtained for CD with and without successive decoding, for TD and for FD. We show that in an M-us&c broadcast system, the outage capacity region is implicitly obtained by deriving the outage probability region for a giveti rate vector. Given the required rate of each user, we find a strategy which bounds the outage probability region for different spectrum-sharing techniques. The corresponding optimal power allocation scheme is a multi-user generalization of the threshold-decision rule for a single-user fading channel. Also discussed is a simpler minimum common outage probability problem under the assumption that the broadcast channel is either not used at all when fading is severe or used simultaneously for all users. Numerical results for various outage capacity regions are obtained for the Nakagami-m fading model.