Specification mining extracts candidate specification from existing systems, to be used for downstream tasks such as testing and verification. Specifically, we are interested in the extraction of behavior models from execution traces. In this paper we introduce mining of branching-time scenarios in the form of existential, conditional Live Sequence Charts, using a statistical data-mining algorithm. We show the power of branching scenarios to reveal alternative scenario-based behaviors, which could not be mined by previous approaches. The work contrasts and complements previous works on mining linear-time scenarios. An implementation and evaluation over execution trace sets recorded from several real-world applications shows the unique contribution of mining branching-time scenarios to the state-of-the-art in specification mining.