  Move-to-front rule is a heuristic updating a list of n items according to
requests. Items are required with unknown probabilities (or popularities). The
induced Markov chain is known to be ergodic. One main problem is the study of
the distribution of the search cost dened as the position of the required item.
Here we first establish the link between two recent papers that both extend
results proved by Kingman on the expected stationary search cost. Combining
results contained in these papers, we obtain the limiting behavior for any
moments of the stationary seach cost as n tends to innity.
