  In the last few years, it became possible to observationally resolve galaxies
with two distinct nuclei in their centre. For separations smaller than 10kpc,
dual and offset active galactic nuclei (AGN) are distinguished: in dual AGN,
both nuclei are active, whereas in offset AGN only one nucleus is active. To
study the origin of such AGN pairs, we employ a cosmological, hydrodynamic
simulation with a large volume of (182Mpc)^3 from the set of Magneticum
Pathfinder Simulations. The simulation self-consistently produces 35 resolved
black hole (BH) pairs at redshift z=2, with a comoving distance smaller than
10kpc. 14 of them are offset AGN and nine are dual AGN, resulting in a fraction
of (1.2 \pm 0.3)% AGN pairs with respect to the total number of AGN. In this
paper, we discuss fundamental differences between the BH and galaxy properties
of dual AGN, offset AGN and inactive BH pairs and investigate their different
triggering mechanisms. We find that in dual AGN the BHs have similar masses and
the corresponding BH from the less massive progenitor galaxy always accretes
with a higher Eddington ratio. In contrast, in offset AGN the active BH is
typically more massive than its non-active counterpart. Furthermore, dual AGN
in general accrete more gas from the intergalactic medium than offset AGN and
non-active BH pairs. This highlights that merger events, particularly minor
mergers, do not necessarily lead to strong gas inflows and thus, do not always
drive strong nuclear activity.
