Contention tree algorithm is initially invented as a solution to improve the stable throughput problem of Slotted ALOHA in multiple access schemes. Even though the throughput is stabilized in tree algorithms, the delay of requests may grow to infinity with respect to the arrival rate of the system. Delay depends heavily on the exploration of the tree structure, i.e., breadth search, or depth search. Breadth search is necessary for faster exploration of tree. The analytical probability distribution of delay, which is available mostly for depth search, is not generalizable to all breadth search. In this paper we fill this gap through though arbitrary grouping of branches and including this in the delay analysis. This enables obtaining the delay analysis of any contention tree algorithm that runs a breadth first search exploration. We show through simulations that the analysis is in agreement with the realizations.