In this paper, we propose a regression tree procedure to estimate the conditional distribution of a variable which is not directly observed due to censoring. The model that we consider is motivated by applications in insurance, including the analysis of guarantees that involve durations, and claim reserving. We derive consistency results for our procedure, and for the selection of an optimal subtree using a pruning strategy. These theoretical results are supported by a simulation study, and two applications to insurance datasets. The first one concerns income protection insurance, while the second deals with reserving in third-party liability insurance.