  Ultra-/hyper-luminous X-ray sources (ULX/HLX) could be interesting
laboratories to improve our understanding of the supermassive black hole growth
through super-Eddington accretion episodes and successive mergers of lighter
holes. ULXs are thought to be powered by super-Eddington accretion on
stellar-mass compact objects, while HLXs may be explained by accretion on
intermediate-mass black holes (IMBHs). However, a significant portion of
ULX/HLX derived from catalog searches are background AGN. Here we build samples
of ULX/HLX from recent XMM-Newton, Swift-XRT and Chandra catalogs and the GLADE
catalog of galaxies. We aim to characterize the frequency, environment and
X-ray properties of ULXs and HLXs to better assess their differences and
understand their populations. After a thorough classification of these X-ray
sources, we remove 42% of S/N>3 sources, shown to be contaminants, to obtain
the cleanest sample of ULX/HLX to date. From a sample of 1342 ULXs and 191
HLXs, we study their frequency, hardness, variability, radial distribution, and
preferred environment. We build their Malmquist-corrected X-ray luminosity
functions (XLF) and compare them with previous studies. The large sample size
allows us to statistically compare ULXs and HLXs and assess differences in
their nature. The interpretation of HLXs as IMBHs is investigated. A
significant break is seen in the XLF at ~$10^{40}$erg/s. Our ULX sample,
containing ~2% of contaminants, confirms that ULXs are located preferentially
in spiral or star-forming galaxies. Some HLXs are significantly softer that
ULXs and XRBs. Unlike ULXs, HLXs seem to reside equally in spiral as well as
lenticular and elliptical galaxies and 35% of them have an optical counterpart.
We estimate their mass and find 120 of them in the range of $2000-10^5
M_\odot$. Most HLXs seem consistent with an accreting massive black hole in a
dwarf galaxy satellite.
