The transfer agent is a company responsible for maintaining the back office operations for a mutual fund. At times a mutual fund will elect to have their custodian bank provide this service, but there are companies that specialize in the functions of the transfer agent.
Unlike the custodian bank which is responsible for overseeing the fund's operation, the transfer agent has a much more limited scope. Its easiest to think of the transfer agent as almost the communications manager for the mutual fund. The transfer agent is responsible for the following: