The broadcast Z channel is a stochastically degraded channel. This work shows that the OR of two symbol streams is a Shannon-limit achieving approach for the broadcast Z channel. Optimality is still maintained if both streams are optimal Z-channel codes and symbols of the second stream are transmitted only when the first stream's symbols are zeros. Using this approach, nonlinear binary turbo codes for the Z-channel that produce codewords with a controlled density of ones are shown to closely approach the capacity-region surface of the broadcast Z channel.  In another optimal appproach, both streams always transmit symbols, but the second stream effectively sees a Z channel with erasures.