We consider the distributed detection problem in trees with unbounded height. The first configuration we studied in this report is a balanced binary relay tree, where the leaves of the tree correspond to N identical and independent sensors. Only the leaves are sensors. The root of the tree represents a fusion center that makes the overall detection decision. Each of the other nodes in the tree are relay nodes that combine two binary messages to form a single output binary message. In this way, the information from the sensors is aggregated into the fusion center via the relay nodes. In Chapter II, we assume that the fusion rules are the unit-threshold likelihood-ratio test which are locally optimal in the sense of minimizing the total error probability after fusion. We describe the evolution of the Type I and Type II error probabilities of the binary data as it propagates from the leaves towards the root. Tight upper and lower bounds for the total error probability at the fusion center as functions of N are derived. These characterize how fast the total error probability converges to 0 with respect to N, even if the individual sensors have error probabilities that converge to 1/2.