EPOCHS XI: The Structure and Morphology of Galaxies in the Epoch of Reionization to z ~ 12.5

We present a structural analysis of 521 galaxy candidates at 6.5 < z < 12.5, with $SNR > 10\sigma$ in the F444W filter, taken from the EPOCHS v1 sample, consisting of uniformly reduced deep JWST NIRCam data, covering the CEERS, JADES GOOD-S, NGDEEP, SMACS0723, GLASS and PEARLS surveys. We use standard software to fit single S\'ersic models to each galaxy in the rest-frame optical and extract their parametric structural parameters (S\'ersic index, half-light radius and axis-ratio), and \texttt{Morfometryka} to measure their non-parametric concentration and asymmetry parameters. We find a wide range of sizes for these early galaxies, but with a strong galaxy-size mass correlation up to $z \sim 12$ such that galaxy sizes continue to get progressively smaller in the high-redshift regime, following $R_{e} = 2.74 \pm 0.49 \left( 1 + z \right) ^{-0.79 \pm 0.08}$ kpc. Using non-parametric methods we find that galaxy merger fractions, classified through asymmetry parameters, at these redshifts remain consistent with those in literature, maintaining a value of $f_{m} \sim 0.12 \pm 0.07$ showing little dependence with redshift when combined with literature at $z > 4$. We find that galaxies which are smaller in size also appear rounder, with an excess of high axis-ratio objects. Finally, we artificially redshift a subsample of our objects to determine how robust the observational trends we see are, determining that observed trends are due to real evolutionary effects, rather than being a consequence of redshift effects.