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We have characterized the underlying stellar host in a sample of 28 bluecompact galaxies (BCGs), by fitting their 2D light distributions. Theirstructural parameters were related with galaxy properties such as colours andgas content. These properties were also compared with those of other galaxytypes. All the BCG hosts but one show low Sersic indexes (0.5 < n < 2), withmean effective radius <$r_{e,B}$>=1.11$\pm$0.74 kpc, and mean surfacebrightness <$\mu_{e,B}$> = 22.59$\pm$0.68 mag arcsec$^{-2}$. Host effectiveradii scale linearly with their luminosity, while n and $\mu_{\rm e}$ do not.In addition, host colours and structural parameters are not linearlycorrelated. Overall,the flux enhancement caused by the starburst is about 0.8mag while their B-R colours decrease by about 0.2 mag. Galaxies with moreluminous and extended hosts show larger and luminous starburst components. BCGhosts show B-R=0.95$\pm$0.26 in median. Overall, BCG hosts are more compact (bya factor ~2) and have higher central surface brightnesses (by about ~2 mag)than dIs and most dEs. BCG hosts and dIs are indistinguishable in the B-bandTully-Fisher relation (TFR). We found that about 50-60 % of the galaxies aremore underluminous than those late-type discs with the same circular velocity.This feature is more important when luminosities are converted into stellarmasses, while it tends to diminish when the HI gas mass is added. Deviationsamong host masses for a given circular velocity from the stellar TFR correlatewith their HI mass-to-luminosity ratio, whereas deviations from the gas+stellarTFR, do not. Overall, our findings suggest that the baryonic mass in BCGs tendsto normal values but BCGs tend to be inefficient producing stars, especiallytoward the low-mass, gas-rich and bluest hosts, in a similar way to dIs.

The Host in Blue Compact Galaxies: Structural Properties and Scaling Relations