Replication of information across multiple servers is becoming a common approach to support popular Web sites. A distributed architecture with some mechanisms to assign client requests to Web servers is more scalable than any centralized or mirrored architecture. In this paper, we consider distributed systems in which the Authoritative Domain Name Server (ADNS) of the Web site takes the request dispatcher role by mapping the URL hostname into the IP address of a visible node, that is, a Web server or a Web cluster interface. This architecture can support local and geographical distribution of the Web servers. However, the ADNS controls only a very small fraction of the requests reaching the Web site because the address mapping is not requested for each client access. Indeed, to reduce Internet traffic, address resolution is cached at various name servers for a time-to-live (TTL) period. This opens an entirely new set of problems that traditional centralized schedulers of parallel/distributed systems do not have to face. The heterogeneity assumption on Web node capacity, which is much more likely in practice, increases the order of complexity of the request assignment problem and severely affects the applicability and performance of the existing load sharing algorithms. We propose new assignment strategies, namely adaptive TTL schemes, which tailor the TTL value for each address mapping instead of using a fixed value for all mapping requests. The adaptive TTL schemes are able to address both the nonuniformity of client requests and the heterogeneous capacity of Web server nodes. Extensive simulations show that the proposed algorithms are very effective in avoiding node overload, even for high levels of heterogeneity and limited ADNS control.