  Nuclear structure functions and cross-sections for heavy flavour production
in lepton-nucleus collisions are investigated in the low $x$ region accessible
now or in the near future. The scattering on a heavy nucleus is described by
the sum of fan diagrams of BFKL pomerons, which is exact in the high-colour
limit. The initial condition for the evolution at $x=0.01$ is taken from a
saturation model, which reproduces the experimental data on the proton. The $A$
dependence of the structure functions is well described by a power factor
$A^\alpha$, with $\alpha$ reaching values as low as 1/2 at extremely low $x$.
The total cross-sections for heavy flavour production reach values of the order
of mb, and the corresponding transverse momentum distributions are sizeable up
to transverse momenta larger than the initial large scale $\sqrt{Q^2+4m_f^2}$.
