  Compact remnants -- stellar mass black holes and neutron stars formed in the
inner few parsec of galactic centres are predicted to sink into the central
parsec due to dynamical friction on low mass stars, forming a high
concentration cusp (Morris 1993). Same physical region may also contain very
high density molecular clouds and accretion discs that are needed to fuel SMBH
activity. Here we estimate gas capture rates onto the cusp of stellar remnants,
and the resulting X-ray luminosity, as a function of the accretion disc mass.
At low disc masses, most compact objects are too dim to be observable, whereas
in the high disc case most of them are accreting at their Eddington rates. We
find that for low accretion disc masses, compact remnant cusps may be more
luminous than the central SMBHs. This ``diffuse'' emission may be of importance
for local moderately bright AGN, especially Low Luminosity AGN. We also briefly
discuss how this expected emission can be used to put constraints on the black
hole cusp near our Galactic Centre.
