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[Abridged] The relation between nuclear star clusters (NSCs) and the growth of the central SMBHs, as well as their connection to the properties of the host galaxies, is crucial for understanding the evolution of galaxies. Recent observations have revealed that about 10 per cent of nucleated galaxies host hybrid nuclei, consisting of both NSCs and accreting SMBHs that power active galactic nuclei (AGN). Motivated by the potential of the recently published multi-wavelength data sets from LeMMINGs survey, here we present the most thorough investigation to date of the incidence of hybrid nuclei in a large sample of 100 nearby nucleated galaxies (10 E, 25 S0, 63 S, and 2 Irr), covering a wide range in stellar mass ($M_{*,\rm gal} \sim 10^{8.7}-10^{12}~\rm M_{sun}$). We identify the nuclei and derive their properties by performing detailed 1D and 2D multi-component decompositions of the optical and near-infrared $HST$ stellar light distributions of the galaxies using S\'ersic and core-S\'ersic models. Our AGN diagnostics are based on homogeneously derived nuclear 1.5 GHz $e$-MERLIN radio, $Chandra$ X-ray (0.3--10 keV) and optical emission-line data. We determine the nucleation fraction ($f_{\rm nuc} $) as the relative incidence of nuclei across the LeMMINGs $HST$ sample and find $f_{\rm nuc} =~ $100/149 (= 67 $\pm$ 7 per cent), confirming previous work, with a peak value of 49/56~(= $88 \pm 13$ per cent) at bulge masses $M_{*,\rm bulge} \sim 10^{9.4}$- $10^{10.8}~\rm M_{sun}$. We identify 30 nucleated LeMMINGs galaxies that are optically active, radio-detected and X-ray luminous ($L_{X} > 10^{39}$ erg s$^{-1}$). This indicates that our nucleated sample has a lower limit $\sim$ 30 per cent occupancy of hybrid nuclei, which is a function of $M_{*,\rm bulge}$ and $M_{*,\rm gal}$. We find that hybrid nuclei have a number density of $(1.5 \pm 0.4) \times 10^{-5}$ Mpc$^{-3}$., Comment: Accepted for publication in MNRAS (21 pages, 10 figures, 9 tables)

We present 1.8 years of near-daily Swift monitoring of the bright, strongly variable Type 1 AGN Fairall 9. Totaling 575 successful visits, this is the largest such campaign reported to date. Variations within the UV/optical are well-correlated, with longer wavelengths lagging shorter wavelengths in the direction predicted by thin disk/lamp-post models. The correlations are improved by detrending; subtracting a second-order polynomial fit to the UV/optical light curves to remove long-term trends that are not of interest to this study. Extensive testing indicates detrending with higher-order polynomials removes too much intrinsic variability signal on reverberation timescales. These data provide the clearest detection to date of interband lags within the UV, indicating that neither emission from a large disk nor diffuse continuum emission from the broad-line region can independently explain the full observed lag spectrum. The observed X-ray flux variations are poorly correlated with those in the UV/optical. Further, subdivision of the data into four ~160 day light curves shows that the UV/optical lag spectrum is highly stable throughout the four periods, but the X-ray to UV lags are unstable, significantly changing magnitude and even direction from one period to the next. This indicates the X-ray to UV relationship is more complex than predicted by the simple reprocessing model often adopted for AGN. A bowl model (lamp-post irradiation and blackbody reprocessing on a disk with a steep rim) fit suggests the disk thickens at a distance (~10 lt-day) and temperature (~8000K) consistent with the inner edge of the BLR., Comment: 20 pages, 9 figures, to appear in ApJ