Large scale coverage holes (CHs) resulting from correlated node failures, can significantly degrade quality of service and also jeopardise the integrity of WSNs. In the absence of centralised control, the distributed relocation of deployed nodes becomes a promising solution especially in harsh and hostile environments. In this paper, a distributed method is proposed that enables a network to partially or entirely repair itself through a collection of distributed movements of disjoint spanned trees (DS-Trees) towards the CHs. DS-Trees are spanned based on the nodes distances from the CHs, which are autonomously perceived by the nodes and their one-hop neighbours. DS-Trees around the CHs are spanned in a downstream style outwards from the holes, as nodes select their parents based on the minimum distance to the CH from their neighbours; nodes then decide whether or not to follow the movements of their DS-Trees parents. To examine the efficiency of the proposed model, its performance is compared with two Voronoi-based and one force-based node relocation algorithms. Results show that the proposed DS-Tree model either outperforms or matches the alternative approaches across a wide range of scenarios.