  We have selected a sample of extremely isolated galaxies (EIGs) from the
local Universe ($\mbox{z} < 0.024$), using a simple isolation criterion: having
no known neighbours closer than $300\,{\rm km\,s}^{-1}$
($3\,h^{-1}\,\mbox{Mpc}$) in the three-dimensional redshift space
$(\alpha,\delta,\mbox{z})$. The sample is unique both in its level of isolation
and in the fact that it utilizes HI redshifts from the Arecibo Legacy Fast ALFA
survey (ALFALFA).
  We analysed the EIG sample using cosmological simulations and found that it
contains extremely isolated galaxies with normal mass haloes which have evolved
gradually with little or no "major events" (major mergers, or major mass-loss
events) in the last $3\,\mbox{Gyr}$. The fraction of EIGs which deviate from
this definition (false positives) is 5%-10%.
  For the general population of dark matter haloes it was further found that
the mass accretion (relative to the current halo mass) is affected by the halo
environment mainly through strong interactions with its neighbours. As long as
a halo does not experience major events, its Mass Accretion History (MAH) does
not depend significantly on its environment. "Major events" seem to be the main
mechanism that creates low-mass subhaloes ($M_{halo} <
10^{10}\,h^{-1}\,M_\odot$) that host galaxies (with $\mbox{M}_{g} \lesssim
-14$).
