  Infrared dark clouds (IRDCs) are potential hosts of the elusive early phases
of high-mass star formation (HMSF). Here we conduct an in-depth analysis of the
fragmentation properties of a sample of 10 IRDCs, which have been highlighted
as some of the best candidates to study HMSF within the Milky Way. To do so, we
have obtained a set of large mosaics covering these IRDCs with ALMA at band 3
(or 3mm). These observations have a high angular resolution (~3arcsec or
~0.05pc), and high continuum and spectral line sensitivity (~0.15mJy/beam and
~0.2K per 0.1km/s channel at the N2H+(1-0) transition). From the dust continuum
emission, we identify 96 cores ranging from low- to high-mass (M = 3.4 to
50.9Msun) that are gravitationally bound (alpha_vir = 0.3 to 1.3) and which
would require magnetic field strengths of B = 0.3 to 1.0mG to be in virial
equilibrium. We combine these results with a homogenised catalogue of
literature cores to recover the hierarchical structure within these clouds over
four orders of magnitude in spatial scale (0.01pc to 10pc). Using supplementary
observations at an even higher angular resolution, we find that the smallest
fragments (<0.02pc) within this hierarchy do not currently have the mass and/or
the density required to form high-mass stars. Nonetheless, the new ALMA
observations presented in this paper have facilitated the identification of 19
(6 quiescent and 13 star-forming) cores that retain >16Msun without further
fragmentation. These high-mass cores contain trans-sonic non-thermal motions,
are kinematically sub-virial, and require moderate magnetic field strengths for
support against collapse. The identification of these potential sites of
high-mass star formation represents a key step in allowing us to test the
predictions from high-mass star and cluster formation theories.
