We see Q civil war in Voyager, and the consequences of it cause unexpected supernovae. It's also implied (via the whole conundrum of "Death Wish") that this isn't the first time the Q have been fighting.

other ones...any competition

The idea only just occurred to me, but it's never actually stated that Q are a specific species, is it? For all we know, "Q" is just what the community of people who reached godlike status have decided to call themselves; each individual member of the continuum could be from any alien species in the galaxy, but once they reach the ability to manipulate time and space to such a degree they can literally require the universe, what they look like hardly matters anymore.