This paper aims to predict some possible futures for the World Wide Web based on several key network parameters: size, complexity, cost and increasing connection speed thorough the uptake of broadband technology. This is done through the production of a taxonomy specifically evaluating the stability properties of the fully-connected star and complete networks, based on the Jackson and Wolinsky (1996) connections model modified to incorporate complexity concerns. We find that when connection speeds are low neither the star nor complete networks are stable, and when connection speeds are high the star network is usually stable, while the complete network is never stable. For intermediate speed levels much depends upon the other parameters. Under plausible assumptions about the future, we find that the Web may be increasingly dominated by a single intermediate site, perhaps best described as a search engine.