1590s, "not limited in extent," from un- (1) "not" + past participle of bound (v.1). Sense of "generous, profuse, liberal" is recorded from 1704. Related: Unboundedness.
unbounded enthusiasm
unbleached
unblemished
unblown
unborn
unbosom
unbounded
unbowed
unbreakable
unbridled
un-British
unbroken