We propose a model of random quantified boolean formulas and their natural random disjunctive logic program counterparts. The model extends the stan- dard models for random SAT and 2QBF. We pro- vide theoretical bounds for the phase transition region in the new model, and show experimentally the presence of the easy-hard-easy pattern. Im- portantly, we show that the model is well suited for assessing solvers tuned to real-world instances. Moreover, to the best of our knowledge, our model and results on random disjunctive logic programs are the first of their kind.