Combining the Hardy-Littlewood k-tuple conjecture with a heuristic application of extreme value statistics, we propose a family of estimator formulas for predicting maximal gaps between prime k-tuples. Extensive computations show that the estimator a log(x/a) − ba satisfactorily predicts the maximal gaps below x, in most cases within an error of ±2a, where a = C_k log^kx is the expected average gap between the same type of k-tuples. Heuristics suggest that maximal gaps between prime k-tuples near x are asymptotically equal to a log(x/a), and thus have the order O(log^k+1x). The distribution of maximal gaps around the “trend” curve a log(x/a) is close to the Gumbel distribution. We explore two implications of this model of gaps: record gaps between primes and Legendre-type conjectures for prime k-tuples.