  We analyze the distribution of eigenvectors for mesoscopic, mean-field
perturbations of diagonal matrices in the bulk of the spectrum. Our results
apply to a generalized $N\times N$ Rosenzweig-Porter model. We prove that the
eigenvectors entries are asymptotically Gaussian with a specific variance,
localizing them onto a small, explicit part of the spectrum. For a well spread
initial spectrum, this variance profile universally follows a heavy-tailed
Cauchy distribution. In the case of smooth entries, we also obtain a strong
form of quantum unique ergodicity as an overwhelming probability bound on the
eigenvectors probability mass. The proof relies on a priori local laws for this
model and the eigenvector moment flow.
