  The dissociation of halo nuclei through their collision with light and heavy
targets is considered within the Continuum Discretized Coupled Channels theory.
We study the one-proton halo nucleus $^8$B and the one-neutron halo nucleus
$^{11}$Be, as well as the more normal $^7$Be. The procedure previously employed
to extract the Coulomb dissociation cross section by subtracting the nuclear
one is critically assessed, and the scaling law usually assumed for the target
mass dependence of the nuclear breakup cross section is also tested. It is
found that the nuclear breakup cross section for these very loosely bound
nuclei does indeed behave as $a+bA^{1/3}$. However, it does not have the
geometrically inspired form of a circular ring which seems to be the case for
normal nuclei such as $^{7}$Be. We find further that we cannot ignore
Coulomb-nuclear interference effects, which may be constructive or destructive
in nature, and so the errors in previously extracted B(E1) using the
subtraction procedure are almost certainly underestimated.
