  We study the evolving environment dependence of mass accretion by dark haloes
in simulations of cold and warm dark matter (CDM and WDM) cosmologies. The
latter allows us to probe the nature of halo growth at scales below the WDM
half-mode mass, which form an extreme regime of nonlinear collisionless
dynamics and offer an excellent test-bed for ideas relating to hierarchical
growth. As environmental proxies, we use the local halo-centric matter density
$\delta$ and tidal anisotropy $\alpha$, as well as large-scale halo bias $b_1$.
Our analysis, while reproducing known trends for environment-dependent
accretion in CDM, as well as the comparison between accretion in CDM and WDM,
reveals several interesting new features. As expected from excursion set
models, WDM haloes have higher specific accretion rates, dominated by the
accretion of diffuse mass, as compared to CDM haloes. For low-mass WDM haloes,
we find that the environment-dependence of both diffuse mass accretion as well
as accretion by mergers is almost fully explained by $\alpha$. For the other
cases, $\delta$ plays at least a comparable role. We detect, for the first
time, a significant and evolving assembly bias due to diffuse mass accretion
for low-mass CDM and WDM haloes (after excluding splashback objects), with a
$z=0$ strength higher than with almost all known secondary variables and
largely explained by $\alpha$. Our results place constraints on semi-analytical
merger tree algorithms, which in turn could affect the predictions of galaxy
evolution models based on them.
