In this visionary and rather personal essay I try to untangle certain ambiguities about tentative origins of molecular biodiversity. A “leitmotif” in my considerations will be the tree-like dendrograms encountered in various evolutionary settings from Darwinian species and replicating genes to the intricate folding patterns of protein domains. These patterns are powerful aids to comprehending present biological diversity, but looking back in evolutionary time may run into difficulties of inconclusive generalization. Extrapolating backward toward the bottom node of tree-like bifurcations, one inevitably ends up in some singularity, where the comparison-based algorithm to construct the tree is virtually stripped for its basic rationale. This is a serious conceptual problem. The following aspects are scrutinized and discussed in this regard for their likely evolutionary beginnings: Darwinian speciation, cells, genomes, fold families of protein domains, and replicating RNA molecules. In some of these examples, the principle that generates the branching pattern loses its predictive power for looking deeper yet, i.e. below the earliest bifurcation events that started to define the diversifying tree. Other and perhaps unthought-of principles may allow escape from such a conceptual impasse. To really comprehend those evolutionary phase transitions we need plausible links to thermodynamically sound reactions in large numbers, and collective coevolution of multiple components should also be considered. To clearly define a common frame of reference, I do not start with Darwin, who only had prescient yet limited access to the basic mechanisms beneath the macroscopic appearance of biodiversity at large, but rather from the Woesean perspective of three fundamentally different superkingdoms (domains or phylodomains) in the universal organismal tree of – presently apparent – life.