One of the critical issues in national research assessment exercises concerns the choice of whether to evaluate the entire scientific portfolio of the institutions or a subset composed of the best products. Under the second option, the capacities of the institutions to select the appropriate researchers and their best products (the UK case) or simply the best products of every researcher (the Italian case) becomes critical, both for purposes of correct assessment of the real quality of research in the institutions evaluated, and for the selective funding that follows. In this work, through case studies of three Italian universities, we analyze the efficiency of the product selection that is intended to maximize the universities' scores in the current national research assessment exercise, the results of which will be the basis for assigning an important share of public financing over the coming years.