The alpha-tree, also known as the quasi-flat zone hierarchy is a widely used representation of images in Mathematical Morphology. This structure organizes the regions according to a similarity criterion into a tree, that eases the multiscale analysis of images. Many alpha-tree algorithms exist and computing this structure efficiently is still an active field of research. Indeed, the alpha-tree is commonly used in remote sensing where there is an urge for fast processing of large terabytes images. In this paper, we propose the first massively parallel alpha-tree algorithm that leverages concurrent union-find data structures to exploit the SIMT (Single Instruction Multiple Threads) programming model of GPUs. Our algorithm outperforms the State-of-the-Art parallel CPU algorithms by a factor of 10 on average on desktop computers and servers. It also opens new perspectives for using Mathematical Morphology methods on GPU pipelines.