Complex search tasks that utilize information from several data sources, are answered by integrating the results of distinct basic search queries. In such integration, each basic query returns a ranked list of items, and the main task is to compute the join of these lists, returning the top-k combinations. Computing the top-k join of ranked lists has been studied extensively for the case where the answer comprises merely complete combinations. However, a join is a lossy operation, and over heterogeneous data sources some highlyranked items, from the results of the basic queries, may not appear in any combination. Yet, such items and the partial combinations in which they appear may still be relevant answers and should not be discarded categorically. In this paper we consider a join where combinations are padded by nulls for missing items. A combination is maximal if it cannot be extended by replacing a null by an item. We present algorithms for computing the top-k maximal combinations...