We present redshift evolution of galaxy effective radius r_e obtained from the HST samples of ~190,000 galaxies at z=0-10. Our HST samples consist of 176,152 photo-z galaxies at z=0-6 from the 3D-HST+CANDELS catalogue and 10,454 LBGs at z=4-10 identified in CANDELS, HUDF09/12, and HFF parallel fields, providing the largest data set to date for galaxy size evolution studies. We derive r_e with the same technique over the wide-redshift range of z=0-10, evaluating the optical-to-UV morphological K-correction and the selection bias of photo-z galaxies+LBGs as well as the cosmological surface brightness dimming effect. We find that r_e values at a given luminosity significantly decrease towards high-z, regardless of statistics choices. For star-forming galaxies, there is no evolution of the power-law slope of the size-luminosity relation and the median Sersic index (n~1.5). Moreover, the r_e-distribution is well represented by log-normal functions whose standard deviation sigma_{ln{r_e}} does not show significant evolution within the range of sigma_{ln{r_e}}~0.45-0.75. We calculate the stellar-to-halo size ratio from our r_e measurements and the dark-matter halo masses estimated from the abundance matching study, and obtain a nearly constant value of r_e/r_vir=1.0-3.5% at z=0-8. The combination of the r_e-distribution shape+standard deviation, the constant r_e/r_vir, and n~1.5 suggests a picture that typical high-z star-forming galaxies have disk-like stellar components in a sense of dynamics and morphology over cosmic time of z~0-6. If high-z star-forming galaxies are truly dominated by disks, the r_e/r_vir value and the disk formation model indicate that the specific angular momentum of the disk normalized by the host halo is j_d/m_d=0.5-1. These are statistical results for galaxies major stellar components, and the detailed study of clumpy sub-components is presented in the paper II.
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