In summary, when a population of disk galaxies with an observed distribution of masses falls in a collapsing cluster in a cosmological setting, a central, giant elliptical galaxy will form in the cluster center. The galaxy forms through the merger of many smaller galaxies which converge on the cluster center along the filamentary structure originating in the initial density field. The one simulation presented here agrees quantitatively in its structure and kinematics with many BCG's but there are still many open questions, in particular: What is the origin of the envelope in the cD galaxies in rich clusters? Perhaps the driving mechanism is tidal stripping (Richstone 1976) and harassment (Moore et al. 1996a) which only occurs in more massive clusters than examined here. Why does BCG central velocity dispersion poorly correlate with the cluster velocity dispersion? Are multiple nuclei in BCG's ongoing mergers or the result of chance projections? How do the properties and the timing of formation of BCG's depend on different cosmological models? If there is a strong dependence, the observation of their evolution may constrain cosmological models. A modest sample of simulations covering different mass scales and cosmological models can answer these questions quantitatively.