  IZw18, ever since regarded as the prototypical blue compact dwarf (BCD)
galaxy, is, quite ironically, the most atypical BCD known. This is because its
large exponential low-surface brightness envelope is not due to an old stellar
host but entirely due to extended nebular emission (ne) (Papaderos et al. 2002;
P02). We study IZw18 and IZw18C down to an unprecedently faint surface
brightness level using HST ACS data.
  We argue that the properties of IZw18C can be consistently accounted for by
propagating star formation over the past ~100 Myr, in combination with stellar
diffusion and the associated radial stellar mass filtering effect (P02).
  As for IZw18, we find that ne extends out to ~16 stellar scale lengths and
provides at least 1/3 of the total optical emission.
  The case of IZw18 suggests caution in studies of distant galaxies in dominant
stages of their evolution, rapidly assembling their stellar mass at high
specific star formation rates (SSFRs). It calls attention to the fact that ne
is not necessarily cospatial with the underlying ionizing and non-ionizing
stellar background, neither has to scale with its surface density. The
prodigious energetic output during dominant phases of galaxy evolution may
result in large exponential ne envelopes, extending much beyond the still
compact stellar component, just like in IZw18. Therefore, the morphological
paradigm of IZw18, while probably unique in the nearby Universe, may be
ubiquitous among high-SSFR galaxies at high redshift. Using IZw18 as reference,
we show that extended ne may introduce substantial observational biases and
significantly affect fundamental galaxy relations. Among others, we show that
the surface brightness profiles of distant morphological analogs to IZw18 may
be barely distinguishable from Sersic profiles with an exponent 2<n<5, thus
mimicking the profiles of massive galaxy spheroids. (abridged)
