  Unstable domain wall (DW) networks in the early universe are cosmologically
viable and can emit a large amount of gravitational waves (GW) before
annihilating. As such, they provide an interpretation for the recent signal
reported by Pulsar Timing Array (PTA) collaborations. A related important
question is whether such a scenario also leads to significant production of
Primordial Black Holes (PBH). We investigate both GW and PBH production using
3D numerical simulations in an expanding background, with box sizes up to
$N=3240$, including the annihilation phase. We find that: i) the network decays
exponentially, i.e. the false vacuum volume drops as $\sim \exp(-\eta^3)$, with
$\eta$ the conformal time; ii) the GW spectrum is larger than traditional
estimates by more than one order of magnitude, due to a delay between DW
annihilation and the sourcing of GWs. We then present a novel semi-analytical
method to estimate the PBH abundances: rare false vacuum pockets of
super-Hubble size collapse to PBHs if their energy density becomes comparable
to the background when they cross the Hubble scale. Smaller (but more abundant)
pockets will instead collapse only if they are close to spherical. This
introduces very large uncertainties in the final PBH abundance. The first
phenomenological implication is that the DW interpretation of the PTA signal is
compatible with observational constraints on PBHs, within the uncertainties.
Second, in a different parameter region, the dark matter can be entirely in the
form of asteroid-mass PBHs from the DW collapse. Remarkably, this would also
lead to a GW background in the observable range of LIGO-Virgo-KAGRA and future
interferometers, such as LISA and Einstein Telescope.
