The evolutionary causes and consequences of allopolyploidization, an exceptional pathway to instant hybrid speciation, are poorly investigated in animals. In particular, when and why hybrid polyploids versus diploids are produced, and constraints on sources of paternal and maternal ancestors, remain underexplored. Using the Palearctic green toad radiation (including bisexually reproducing species of three ploidy levels) as model, we generate a range-wide multi-locus phylogeny of 15 taxa and present four new insights: (i) At least five (up to seven) distinct allo-triploid and allo-tetraploid taxa have evolved in the Pleistocene; (ii) All maternal and paternal ancestors of hybrid polyploids stem from two deeply diverged nuclear clades (6 Mya, 3.1-9.6 Mya), with distinctly greater divergence than the parental species of diploid hybrids found at secondary contact zones; (iii) Allotriploid taxa possess two conspecific genomes and a deeply-diverged allospecific one, suggesting that genomic imbalance and divergence are causal for their partly clonal reproductive mode; (iv) Maternal vs. paternal genome contributions exhibit asymmetry, with the maternal nuclear (and mitochondrial) genome of polyploids always coming from the same clade, and the paternal genome from the other. We compare our findings with similar patterns in diploid/polyploid vertebrates, and suggest deep ancestral divergence as a precondition for successful allopolyploidization.