  Massive black holes (MBHs) are typically hosted in the centres of massive
galaxies but they appear to become rarer in lower mass galaxies, where nuclear
star clusters (NSCs) frequently appear instead. The transition region, where
both an MBH and NSC can co-exist, has been poorly studied to date and only a
few dozen galaxies are known to host them. One avenue for detecting new
galaxies with both an MBH and NSC is to look for accretion signatures of MBHs.
Here, we use new SRG/eROSITA all-sky survey eRASS:4 data to search for X-ray
signatures of accreting MBHs in NSCs, while also investigating their combined
occupation fraction. We find significant detections for 18 galaxies (~8.3%),
including one ultra-luminous X-ray source; however, only three galaxies
(NGC2903, 4212, and 4639) have X-ray luminosities that are higher than the
expected value from X-ray binaries, indicative of the presence of an MBH. In
addition, the X-ray luminosity of six galaxies (NGC2903, 3384, 4321, 4365,
4639, and 4701) differs from previous studies and could indicate the presence
of a variable active galactic nucleus. The combined occupation fraction of
accreting MBHs and NSCs becomes non-zero for galaxy masses above ~10^7.5 M_sun
and this result is slightly elevated as compared to the literature data. Our
data extend, for the first time, towards the dwarf elliptical galaxy regime and
identify promising MBH candidates for higher resolution follow-up observations.
At most galaxy masses (and with the exception of three cases), the X-ray
constraints are consistent with the expected emission from binary systems or an
Eddington fraction of at most 0.01%, assuming a black holes mass of 10^6.5
M_sun. This work confirms the known complexities in similar-type of studies,
while providing the appealing alternative of using X-ray survey data of
in-depth observations of individual targets with higher resolution instruments.
