objS{ZW I 18}{I Zw 18}, ever since regarded as the prototypical blue compact dwarf (BCD) galaxy, is, quite ironically, the most atypical BCD known. This is because its large low-surface brightness (LSB) envelope is not due to an old underlying stellar host, as invariably is the case for typical BCDs, but is entirely due to extended nebular emission. Our goal is to explore
I Zw 18 and its detached C component
I Zw 18C down to an unprecedently faint surface brightness µ (mag/"
2) level in order to gain further insight into the structural properties and evolutionary history of this enigmatic galaxy pair. We present a photometric analysis of the entire set of archival HST ACS V, R and I band data for
I Zw 18. Radial color profiles for
I Zw 18C reveal blue and practically constant colors (0±0.05) down to µ∼27.6, and a previously undisclosed, slightly redder (V-I≃0.2), stellar population in its extreme periphery (µ∼29). We argue that stellar diffusion over τ∼10
8 yr and the associated stellar mass filtering effect can consistently account for the observed properties of the stellar component in the outskirts of
I Zw 18C. This process, in combination with propagating star formation with a mean velocity of ∼20km/s can reproduce all essential characteristics of
I Zw 18C within ~τ. An extremely faint substrate of older stars cannot be ruled out but does not need to be postulated. As for
I Zw 18, we find that nebular emission (ne) extends out to ∼16 stellar scale lengths, shows a nearly exponential outer profile, and provides at least one third of the total optical emission. Nebular emission dominates already at µ∼23.5, as evident from e.g. the uniform and extremely blue (V-I≃-1, R-I≃-1.4) colors of the LSB envelope of
I Zw 18. The case of
I Zw 18 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 of ne not necessarily being cospatial with the underlying ionizing and non-ionizing stellar background. It also does not have to scale with the background 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
I Zw 18. Therefore, the morphological paradigm of
I Zw 18, while probably unique in the nearby Universe, may be ubiquitous among high-SSFR galaxies at high redshift. Using
I Zw 18 as reference, we show that extended ne may introduce substantial observational biases and affect several of the commonly studied fundamental galaxy relations. Among others, we show that the surface brightness profiles of distant morphological analogs to
I Zw 18 may be barely distinguishable from Sersic profiles with an exponent 2≲η≲5, thus mimicking the profiles of massive galaxy spheroids.
