Using kinematical and new structural data of a sample of 27 Giant HII regions (GHIIR) and 103 HII galaxies (HIIG), I explore the relations between their size, surface brightness, ionized gas velocity dispersion, metallicity, excitation and extinction. I find that the size is well described by the combination of two parameters: the velocity dispersion (σ) and the average surface brightness (⟨Ie⟩) with no indication for the further need of extra parameters. This description corresponds to that of a narrow plane in the logarithmic 3D space [Size, σ, ⟨Ie⟩] with a thickness consistent with observational errors. This ``Fundamental Plane" resembles that of massive spheroidal galaxies suggesting that similar processes may be at play. The thinness of the fundamental plane of HIIG and GHIIR suggests its potential use as a standard ruler distance indicator in the future with improved observations.
I also present the comparison of the Star Formation Rate (SFR) of HIIGs with other star-forming galaxies as Blue Compact Dwarfs and GPs. The results show that each set of this "kind" of galaxies is just a subsample with a narrow redshift range of a larger HIIGs sample.
On the other hand, I present one application of Integral Field Spectroscopy to estimate the Star Formation Rate in type-1 AGN hosts galaxies making use of deblending of AGN and host galaxy. The approximations to the quasar-host deblending are presented and the derivation of spatially resolved maps of emission narrow lines and the estimation of the SFR. In two of the analyzed galaxies, the results show SFR values comparable to those obtained from the infrared luminosity via SED fitting.