  Models of the decoupling of baryons and photons during the recombination
epoch predict the existence of a large-scale velocity offset between baryons
and dark matter at later times, the so-called streaming velocity. In this
paper, we use high resolution numerical simulations to investigate the impact
of this streaming velocity on the spin and shape distributions of high-redshift
minihalos, the formation sites of the earliest generation of stars. We find
that the presence of a streaming velocity has a negligible effect on the spin
and shape of the dark matter component of the minihalos. However, it strongly
affects the behaviour of the gas component. The most probable spin parameter
increases from $\sim$0.03 in the absence of streaming to $\sim$0.15 for a run
with a streaming velocity of three times $\sigma_{\rm rms}$, corresponding to
1.4 km\,s$^{-1}{}$ at redshift $z=15$. The gas within the minihalos becomes
increasingly less spherical and more oblate as the streaming velocity
increases, with dense clumps being found at larger distances from the halo
centre. The impact of the streaming velocity is also mass-dependent: less
massive objects are influenced more strongly, on account of their shallower
potential wells. The number of halos in which gas cooling and runaway
gravitational collapse occurs decreases substantially as the streaming velocity
increases. However, the spin and shape distributions of gas that does manage to
cool and collapse are insensitive to the value of the streaming velocity and we
therefore do not expect the properties of the stars that formed from this
collapsed gas to depend on the value of the streaming velocity. The spin and
shape of this central gas clump are uncorrelated with the same properties
measured on the scale of the halo as a whole.
