We study the characteristics of Bose-Einstein condensates formed by the act
ion of three different potentials: Newtonian self-gravity, hard-sphere repu
lsion (the Gross-Pittaevski potential), and a harmonic trap potential as us
ed in laboratory experiments. We show that in a certain regime a condensate
can form which is much larger than predicted by the quantum self-gravitati
onal ground state radius. Furthermore, the size is independent of the numbe
r of particles in the condensate. We speculate that massive objects of this
type may form in extreme isolation through gravitational accretion onto a
fixed-size object. We propose that these be called deep-space quantum objec
ts, or DSQOs (discos). Analytical Hartree-Fock solutions for the DSQO groun
d state are obtained, along with a formula for the Limiting DSQO radius and
energy. These are then compared with numerical calculations. Prospects for
DSQO formation are briefly discussed with emphasis on possible cooling mec
hanisms and the dynamic stability of structures formed by accretion.