  The hypernetted chain/mean spherical approximation (HNC/MSA) integral
equation is obtained and solved numerically for a totally asymmetric primitive
model electrolyte around a spherical macroparticle. The ensuing radial
distribution functions show a very good agreement when compared to our Monte
Carlo and molecular dynamics simulations for spherical geometry and with
respect to previous anisotropic reference HNC calculations in the planar limit.
We report an analysis of the potential vs charge relationship, radial
distribution functions, mean electrostatic potential and cumulative reduced
charge for representative cases of 1:1 and 2:2 salts with a size asymmetry
ratio of 2. Our results are collated with those of the Modified Gouy-Chapman
(MGC) and unequal radius Modified Gouy-Chapman (URMGC) theories and with those
of HNC/MSA in the restricted primitive model (RPM) to assess the importance of
size asymmetry effects. One of the most striking characteristics found is
that,\textit{contrary to the general belief}, away from the point of zero
charge the properties of an asymmetric electrical double layer (EDL) are not
those corresponding to a symmetric electrolyte with the size and charge of the
counterion, i.e. \textit{counterions do not always dominate}. This behavior
suggests the existence of a new phenomenology in the EDL that genuinely belongs
to a more realistic size-asymmetric model where steric correlations are taken
into account consistently. Such novel features can not be described by
traditional mean field theories like MGC, URMGC or even by enhanced formalisms,
like HNC/MSA, if they are based on the RPM.
