  We analyze 26 Luminous Compact Blue Galaxies (LCBGs) in the HST/ACS Ultra
Deep Field (UDF) at z ~ 0.2-1.3, to determine whether these are truly small
galaxies, or rather bright central starbursts within existing or forming large
disk galaxies. Surface brightness profiles from UDF images reach fainter than
rest-frame 26.5 B mag/arcsec^2 even for compact objects at z~1. Most LCBGs show
a smaller, brighter component that is likely star-forming, and an extended,
roughly exponential component with colors suggesting stellar ages >~ 100 Myr to
few Gyr. Scale lengths of the extended components are mostly >~ 2 kpc, >1.5-2
times smaller than those of nearby large disk galaxies like the Milky Way.
Larger, very low surface brightness disks can be excluded down to faint
rest-frame surface brightnesses (>~ 26 B mag/arcsec^2). However, 1 or 2 of the
LCBGs are large, disk-like galaxies that meet LCBG selection criteria due to a
bright central nucleus, possibly a forming bulge. These results indicate that
>~ 90% of high-z LCBGs are small galaxies that will evolve into small disk
galaxies, and low mass spheroidal or irregular galaxies in the local Universe,
assuming passive evolution and no significant disk growth. The data do not
reveal signs of disk formation around small, HII-galaxy-like LCBGs, and do not
suggest a simple inside-out growth scenario for larger LCBGs with a disk-like
morphology. Irregular blue emission in distant LCBGs is relatively extended,
suggesting that nebular emission lines from star-forming regions sample a major
fraction of an LCBG's velocity field.
