Context :

Aims : We characterise the underlying stellar host in a sample of 20 blue compact galaxies ( BCGs ) , by fitting their two-dimensional light distributions .
Their derived host structural parameters and those of eight other BCGs already obtained in a previous paper are related to galaxy properties , such as colours and gas content .
These properties are also compared with those of other galaxy types .

Methods : The structural parameters of the host were derived by fitting a two-dimensional PSF-convolved Sérsic model to deep optical images in several bandpasses ( B , V , R , I ) .
We followed a fitting technique that consists in the accurate masking-out of the star-forming regions in several steps .

Results : All the BCG hosts but one show low Sérsic indexes ( 0.5 \la n \la 2 ) , with mean effective radius < r _ { e,B } > = 1.11 \pm 0.74 kpc and mean surface brightness < \mu _ { e,B } > = 22.59 \pm 0.68 mag arcsec ^ { -2 } .
Host effective radii scale linearly with their luminosity , while n and \mu _ { e } do not .
In addition , host colours and structural parameters are not linearly correlated .
Overall , the flux enhancement caused by the starburst is about 0.8 mag , while their B - R colours decrease by about 0.2 mag .
Galaxies with more luminous and extended hosts show larger and luminous starburst components , whereas the relative strength of the burst ( L _ { burst } / L _ { host } ) does not show any significant dependence on the host luminosity ( or mass ) .
While hosts show B - R = 0.95 \pm 0.26 in median , galaxies with redder hosts ( < B - R > = 1.29 \pm 0.10 ) and with bluer hosts ( < B - R > = 0.66 \pm 0.10 ) are distinguished among the more and less luminous systems , respectively .
Overall , BCG hosts are more compact ( by a factor \sim 2 ) and have higher central surface brightnesses ( by about \sim 2 mag ) than dIs and most dEs .
BCG hosts and isolated dIs are indistinguishable in the B -band Tully–Fisher relation ( TFR ) .
We found that about 50–60 % of the galaxies are more underluminous than those late-type discs with the same circular velocity .
This feature is more important when luminosities are converted into stellar masses , while it tends to diminish when the H i gas mass is added .
Deviations among host masses for a given circular velocity from the stellar TFR correlate with their H i mass-to-luminosity ratio ( M _ { HI } / L _ { B } ) , whereas deviations from the gas + stellar TFR do not .
Overall , our findings suggest that the baryonic mass in BCGs tends to normal values , but BCGs tend to be inefficient by producing stars , especially toward the low-mass , gas-rich , and bluest hosts , in a similar way to dIs .

Conclusions :