While both Kant and Laplace are credited with the theory, Laplace's explanation was more detailed and gained greater acceptance in the scientific community. He proposed that the solar system formed from a rotating cloud of gas and dust (a nebula), which contracted under its own gravity. As the cloud contracted, it spun faster, flattening into a disk. The center of the disk eventually formed the Sun, while the remaining material clumped together to form the planets.
Therefore, while Kant is recognized for the initial concept, Laplace's contribution in providing a more refined and detailed explanation is what ultimately led to the widespread acceptance of the dust cloud theory.