We present a heuristic algorithm for the run-time distribution of task sets in a homogeneous Multiprocessor network-on-chip. The algorithm is itself distributed over the processors and thus can be applied to systems of arbitrary size. Also, tasks added at run-time can be handled without any difficulty, allowing for inline optimisation. Based on local information on processor workload, task size, communication requirements, and link contention, iterative decisions on task migrations to other processors are made. The mapping results for several example task sets are first compared with those of an exact (enumeration) algorithm with global information for a 3×3 processor array. The results show that the mapping quality achieved by our distributed algorithm is within 25% of that of the exact algorithm. For larger array sizes, simulated annealing is used as a reference and the behaviour of our algorithm is investigated. The mapping quality of the algorithm can be shown to be within a reasonable range (below 30% mostly) of the reference. This adaptability and the low computation and communication overhead of the distributed heuristic clearly indicate that decentralised algorithms are a favourable solution for an automatic task distribution.