When Captain Marvel Jr discovered he had a relative with powers of his own
Back in the early 1940's Fawcett's Comics, Freddy Freeman became Captain Marvel Jr when Captain Marvel saved his life after an attack by Captain Nazi and shared soem of his SHAZAM! based powers with him.
At much the same time, over in Quality Comics, their new hero Kid Eternity, was given his powers when an angel accidentally took his soul to Heaven when he should have survived.
Both used the "Magic word transformation" approach.
Saying "Captain Marvel" turned Freddy into Captain Marvel Jr. with strength, speed, flight, stamina, wisdom and power.
The boy known only as "Kid" assumed his powers when he spoke the word "Eternity", able to become invisible, intangible, fly (Think Danny Phantom I guess) and most importantly, summon up any character from history or legend to aid him. And he was always accompanied by "Mr Keeper", the angelic being who had made the initial error, and who Kid needed to be near to use his powers too.
There's a terrrific article on this over at CBR, so I'd recommend a read
There was no connetion between the characters (though based on the link above, neither creator was entirely unaware of the other)
By 1977, DC Comics had bought both Fawcett and Quality and so, in their Earth-S based world where the Marvel Family were the pre-eminent super-heroes, they also introduced the Quality characters too, like Kid Eternity.
Since Billy and the Kid both share the same issue of needing to speak to activate their powers, they both end up tied up, gagged and in a deathtrap, but that was par for the course for both of them.
Say what you will, that henchman is REALLY earning his pay today!
At any rate, they both survive, but that was Kid Eternity's only appearance until 1982.
In the run up to his reintroduction into the still Earth-S based Captain Marvel series, a number of cases over several months feature the sudden an inexplicable appearance of people who were either dead, or were from legends.
Until they finally realise who it must be, though they don't suspect why
Which is quite the lead in to the next issue, no?
E Nelson Bridwell then crafts one of the most elegant retcons I have ever seen.
And I also want to gush again about Don Newton, the artist on this story, who was a lifelong fan of Captain Marvel, and who left us far too soon. His clean lines and super-expressive body langauge was always a treat, and perfect for the Marvel Family (though he also did gorgeous work on other titles, including a memorable run on Batman, during the later stages of Dick Grayson's Robin and the original introduction of Jason Todd, but that's another story...)
Anyway, back to the plot at hand.
After these appearances, he pretty much disappeared, apart from a cameo, along with the rest of the DCU, in Crisis on Infinite Earths just before Earth-S was dissolved and merged with the main DCU.
He did, sort of, get rebooted, in the 1991 Grant Morrison Kid Eternity miniseries which was part of the mature-reader Vertigo line and added a very cynical, 90's "Too cool for school" vibe.
It included some fairly groundbreaking art by Duncan Fegredo, but only kept parts of the concept, and recontextualised the character's history, including losing the link to Freddy, and making it so he had actually been an unwitting agent of chaotic demons the whole time... it was a whole thing.
I include a sample here for context, and because the art was quite something.
Kid Eternity has been brought back a couple of times since then, reinvented, or restored to more classic look, though not always treated well
He was introduced and killed off in Geoff Johns JSA
Brought back and REkilled in the post Infinite Crisis Teen Titans
Reimagined as a coroner in the New52
Though I'm told a new, female Kid Eternity has shown up recently, who I've not come across yet.
Anyway, thank you for coming to my TED talk on Kid Eternity! :)