We have performed hydrodynamical simulations from cosmological initial conditions using the AMR code RAMSES to study atomic cooling haloes ( ACHs ) at z = 10 with masses in the range 5 \times 10 ^ { 7 } { M _ { \odot } } ~ { } \hbox to 0.0 pt { $ < $ } { \lower 4.3 pt \hbox { $ \sim$ } } % M~ { } \hbox to 0.0 pt { $ < $ } { \lower 4.3 pt \hbox { $ \sim$ } } 2 \times 10 ^ { 9 } { M _ { % \odot } } .
We assume the gas has primordial composition and { H _ { 2 } } -cooling and prior star-formation in the haloes have been suppressed .
We present a comprehensive analysis of the gas and DM properties of 19 haloes at a spatial resolution of \sim 10 ( proper ) pc , selected from simulations with a total volume of \sim 2000 ( comoving ) Mpc ^ { 3 } .
This is the largest statistical hydro-simulation study of ACHs at z > 10 to date .
We examine the morphology , angular momentum , thermodynamical state , and turbulent properties of these haloes , in order to assess the prevalence of disks and massive overdensities that may lead to the formation of supermassive black holes ( SMBHs ) .
We find no correlation between either the magnitude or the direction of the angular momentum of the gas and its parent DM halo .
Only 3 of the haloes form rotationally supported cores .
Two of the most massive haloes , however , form massive , compact over-dense blobs , which migrate to the outer region of the halo .
These blobs have an accretion rate \sim { 0.5 M _ { \odot } yr ^ { -1 } } ( at a distance of 100 pc from their center ) , and are possible sites of SMBH formation .
Our results suggest that the degree of rotational support and the fate of the gas in a halo is determined by its large-scale environment and merger history .
In particular , the two haloes that form over-dense blobs are located at knots of the cosmic web , cooled their gas early on ( z > 17 ) , and experienced many mergers .
The gas in these haloes is thus lumpy and highly turbulent , with Mach numbers { \mathcal { M } } \ga 5 .
In contrast , the haloes forming rotationally supported cores are relatively more isolated , located midway along filaments of the cosmic web , cooled their gas more recently , and underwent fewer mergers .
As a result , the gas in these haloes is less lumpy and less turbulent ( Mach numbers { \mathcal { M } } \la 4 ) , and could retain most of its angular momentum .
The remaining 14 haloes have a diverse range of intermediate properties .
If verified in a larger sample of haloes and with additional physics to account for metals and star-formation , our results will have implications for observations of the highest-redshift galaxies and quasars with JWST .