This paper presents how to perform minimax optimal classification, regression, and density estimation based on fixed-(k) nearest neighbor (NN) searches. We consider a distributed learning scenario, in which a massive dataset is split into smaller groups, where the (k)-NNs are found for a query point with respect to each subset of data. We propose optimal rules to aggregate the fixed-(k)-NN information for classification, regression, and density estimation that achieve minimax optimal rates for the respective problems. We show that the distributed algorithm with a fixed (k) over a sufficiently large number of groups attains a minimax optimal error rate up to a multiplicative logarithmic factor under some regularity conditions. Roughly speaking, distributed (k)-NN rules with (M) groups has a performance comparable to the standard (\Theta(kM))-NN rules even for fixed (k).