Accretion of matter onto central Black Holes (BHs) in galaxies liberates enormous amounts of feedback energy,
which influence the formation and evolution of structures, affecting the environment from pc to Mpc scales.
These BHs are usually Supermassive BHs (SMBHs: mass $\geq 10^6 M_{\odot}$)
existing at the centers of active galactic nuclei (AGN),
which are widely observed through their multi-wavelength emission at all cosmic epochs.
The SMBH energy output is often observed as powerful AGN outflows in a wide variety of forms.
Relatively recently, Intermediate-Mass BHs (IMBHs: mass = $100 - 10^6 M_{\odot}$)
have started to be observed hosted in Dwarf Galaxy (DG) centers.
Some of the central IMBHs in DGs show signatures of activity in the form of low-luminosity AGN.

We have performed Cosmological Hydrodynamical Simulations to probe SMBHs in high-z quasars \cite{Barai17},
and IMBHs in DGs \cite{BaraiPino18}.
Our simulations employ the 3D TreePM SPH code GADGET-3, and include metal cooling, star formation,
chemical enrichment, stellar evolution, supernova feedback, AGN accretion and feedback.
Analyzing the simulation output in post-processing, we investigate the growth of the first IMBHs,
and the growth of the first SMBHs, their impact on star-formation,
as well as their co-evolution with the respective host galaxies.
We quantify the impact of SMBHs and IMBHs on their host galaxies,
especially the effects on quenching star-formation.
We also study the corresponding BH outflow properties.