By identifying the k largest or smallest elements in a set of data, top-k selection is critical for modern high-performance databases and machine learning systems, especially with large data volumes. However, previous studies on its GPU implementation are mostly merge-based and rely heavily on the high-speed but size-limited on-chip memory, thereby resulting in a restricted upper bound on k. This paper introduces RadiK, a highly optimized GPU-parallel radix top-k selection that is scalable with k, input length, and batch size. With a carefully designed optimization framework targeting high memory bandwidth and resource utilization, RadiK supports far larger k than the prior art, achieving up to 2.5x speedup for non-batch queries and up to 4.8x speedup for batch queries. We also propose a lightweight refinement that strengthens the robustness of RadiK against skewed distributions by adaptively scaling the input elements.