  We study the sizes, angular momenta and morphologies of high-redshift
galaxies using an update of the Meraxes semi-analytic galaxy evolution model.
Our model successfully reproduces a range of observations from redshifts
$z=0$-$10$. We find that the effective radius of a galaxy disc scales with UV
luminosity as $R_e\propto L_{\textrm{UV}}^{0.33}$ at $z=5$-$10$, and with
stellar mass as $R_e\propto M_\ast^{0.24}$ at $z=5$ but with a slope that
increases at higher redshifts. Our model predicts that the median galaxy size
scales with redshift as $R_e \propto (1+z)^{-m}$, where $m=1.98\pm0.07$ for
galaxies with $(0.3$-$1)L^\ast_{z=3}$ and $m=2.15\pm0.05$ for galaxies with
$(0.12$-$0.3)L^\ast_{z=3}$. We find that the ratio between stellar and halo
specific angular momentum is typically less than one and decreases with halo
and stellar mass. This relation shows no redshift dependence, while the
relation between specific angular momentum and stellar mass decreases by
$\sim0.5$ dex from $z=7$ to $z=2$. Our model reproduces the distribution of
local galaxy morphologies, with bulges formed predominantly through galaxy
mergers for low-mass galaxies, disc-instabilities for galaxies with
$M_\ast\simeq10^{10}$-$10^{11.5}M_\odot$, and major mergers for the most
massive galaxies. At high redshifts, we find galaxy morphologies that are
predominantly bulge-dominated.
