When Linda Danvers tried to take the place of pre-Crisis Kara Zor-El, she unknowingly won the heart of the pre-Crisis version of Superman. The two married, and had a daughter named Ariella Kent (R'E'L in Kryptonian). When Spectre came to send Linda back to the post-Crisis era, and return the pre-Crisis to its original state (and replace her with Kara), Linda agreed on the condition that Ariella would be spared. The Spectre agreed to her terms, and when all traces of Linda Danvers' existence was wiped from the pre-Crisis era, Ariella was left alone to wander the universe. Possessing incredible powers at the very tender age of 6, Ariella began to play in space, unknowingly causing massive devastation. Her ability to time-travel carried her to the 853rd century, where she saved a planet from destruction by playing with the invaders (and accidentally destroying all of their ships and weapons). She became very attached to alien refugee, Dura, who had been fleeing from her, since she had nearly destroyed his planet. She called him "Daddy" (he called her "R'E'L, the Destroyer of Worlds"), and he was able to use her affection to exert some degree of control over her, and keep the universe safe.
Later, she time-traveled to the post-Crisis era, shortly after the "Sins of Youth" storyline, and met her newest playmate, Klarion the Witch Boy (who seemed smitten with the 6-and-a half year old powerhouse). Her whereabouts are unknown, but it is assumed she is still having adventures somewhere.
A hybrid of metahuman/Kryptonian heritage, Ariella possesses vast powers for her young age. She has incredible superhuman strength and speed. She can fly, travel through time at will, move objects via telekinesis, teleport anywhere she wishes, and even create duplicates of her self. She is invulnerable, and ages at an extremely slow rate. She also has X-ray vision and heat vision. Due to her high-level of power, and young age, Ariella can be highly destructive, as she hasn't learned to hold back her abilities.
According to an interview with Newsarama, following the events of Infinite Crisis, Didio stated that the Matrix Supergirl was wiped from existence. However, Geoff Johns later stated, "As for this...huh? Linda Danvers hasn't been retconned out at all."  The future(and past) of Linda Danvers, therefore of Ariella, remains uncertain.