  In order to elucidate the origin of spin in both dark matter and baryons in
galaxies, we have performed hydrodynamical simulations from cosmological
initial conditions. We study atomic cooling haloes in the redshift range $100 >
z > 9$ with masses of order $10^9{\rm M_{\odot}}$ at redshift $z=10$. We assume
that the gas has primordial composition and that ${\rm H_2}$-cooling and prior
star-formation in the haloes have been suppressed. We present a comprehensive
analysis of the gas and dark matter properties of four halos with very low
($\lambda \approx 0.01$), low ($\lambda \approx 0.04$), high ($\lambda \approx
0.06$) and very high ($\lambda \approx 0.1$) spin parameter. Our main
conclusion is that the spin orientation and magnitude is initially well
described by tidal torque linear theory, but later on is determined by the
merging and accretion history of each halo. We provide evidence that the
topology of the merging region, i.e. the number of colliding filaments, gives
an accurate prediction for the spin of dark matter and gas: halos at the center
of knots will have low spin while those in the center of filaments will have
high spin. The spin of a halo is given by $\lambda \approx 0.05 \times
\left(\frac{7.6}{\rm number\,\,\, of \,\,\, filaments}\right)^{5.1}$.
