are there any conclusions on atherun and cagalli's relationship in gundam?

Answer 1

Gundam Seed and Seed Destiny
Spoiler alert!
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That being said, I could move on and elaborate on their relationship. At the end of Gundam seed, fans speculate that both of them are truly lovers and that fact was emphasized at the first coul of Seed Destiny when Athrun gave a ring to Cagalli. Even Yuuna (Cagalli's "fiance") mentioned about how bad it is for her to have a coordinator boyfriend. Either way, we all know that Cagalli loves Athrun. But, a strange thing happened by the last coul of the series, the story suddenly shifted to a discreet Athrun x Meyrin pairing which was seen up until the end of the special Final Phase TV episode.

According to the director and scriptwriter, the Athrun x Cagalli relationship was never officially planned unlike the Kira x Lacus one. Although fans argue that they do really like each other. But some also say that at the end of Destiny, Cagalli chose her political duties rather than Athrun since he doesn't have the power yet to protect her and Orb.

In short, their relationship is truly unknown as speculations are far more numerous. But fans do like them together and that would likely affect the future sequels of this series. Possibly the upcoming Gundam Seed movie too--> announced last month at the Sony Music Anime Fes. in Tokyo and yesterday at Osaka.

Answer 2

There is a new OVA (Final Plus) was aired on Christmas Day that tied up some loose ends in the Cosmic Era storyline.

The OVA added in a scene where Cagalli embraced all of her friends one-by-one before they left Earth, including Athrun.

This is shown after the scene in episode 45 where Cagalli removed her promise/engagement ring Athrun gave her. Overall, the scene did show Athrun and Cagalli fans hope for the future, though it appears she is not shown wearing the ring again.

She has apparently decided her duties to Orb are more important at this time than her romantic relationship with Athrun. Though the relationship is a work in progress and Meyrin and Athrun are not romantically together at the end of Final Plus, Cagalli's absence from the final scenes of Final Plus that involve Athrun is suspect that the Athrun and Cagalli relationship will need a lot of work in future.

More substantial closure/restoration of the matter may be covered in the upcoming Destiny Special Edition, which is said to retell the story solely from Athrun's point of view.

So in the end (for now), there's no conclusion in Athrun/Cagalli relationship. Cagalli is too busy in politics (just like Heero/Relena ^_^)