Understanding the nature of the accretion disk, its interplay with the x-ray corona, and assessing black hole spin demographics remain open challenges in astrophysics. In this paper, we examine the predictions of the standard $\alpha$-disk model, origin of the puzzling soft x-ray excess, and measure the black hole spin parameter by applying an updated high-density disk reflection model to the XMM-Newton/NuSTAR broadband (0.3–78 keV) x-ray spectra of a sample of 11 type-1 active galactic nuclei (AGN). Our Bayesian analysis confirms that a variable-density relativistic disk reflection model with a broken power-law emissivity profile can simultaneously fit the soft x-ray excess, broad iron K line emission, and Compton hump in three out of 11 AGN. For the remaining sources, a distinct warm Comptonization component is still required, which supports a hybrid origin for the soft x-ray excess. The measured temperature and optical depth of the warm corona span nearly the entire theoretically allowed range, with median values of ${0.43}_{-0.18}^{+0.40}\mathrm{keV}$ and ${12.5}_{-3.9}^{+3.1}$, respectively. Our first systematic calculation of the disk-to-corona power transfer fraction reveals that the fraction of power released from the accretion disk into the hot corona spans a wide range, with a sample median of ${0.68}_{-0.25}^{+0.25}$. The sample median values for the hot coronal plasma temperature and optical depth are ${54}_{-12}^{+11}\mathrm{keV}$ and ${0.98}_{-0.28}^{+0.22}$, respectively. Finally, through both hard x-ray (3–78 keV) and broadband (0.3–78 keV) relativistic reflection spectroscopy, we systematically constrain the black hole spin parameter across the mass scales of $\log (M_{\mathrm{BH}}/M_{\odot })\sim 5.5–9.0$, thereby increasing or refining the available spin measurements in the AGN population by $\sim 20\%$.

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• General relativity
• X ray astronomy
• Accretion disk & black-hole plasma
• Astronomical black holes
• Galactic nuclei & quasars