  Condensation phenomena in particle systems typically occur as one of two
distinct types: either as a spontaneous symmetry breaking in a homogeneous
system, in which particle interactions enforce condensation in a randomly
located site, or as an explicit symmetry breaking in a system with background
disorder, in which particles condensate in the site of extremal disorder. In
this paper we confirm a recent conjecture by Godr\`eche and Luck by showing,
for a zero range process with weak site disorder, that there exists a phase
where condensation occurs with an intermediate type of symmetry-breaking, in
which particles condensate in a site randomly chosen from a range of sites
favoured by disorder. We show that this type of condensation is characterised
by the occurrence of a Gamma distribution in the law of the disorder at the
condensation site. We further investigate fluctuations of the condensate size
and confirm a phase diagram, again conjectured by Godr\`eche and Luck, showing
the existence of phases with normal and anomalous fluctuations.
