While the Vasari capital carrier has a great fleet repair ability (only hull) and the Vasari overseers are perhaps the best support cruiser for caps (250 hp and extra armor), if it was healing shields and at a fast rate what you were probably seeing was the Devastator's ultimate ability. I think it is called disintegration and it does massive damage to one ship and gets a huge shield and hull restore buff, to the point that it is usually fully healed (just the devastator). This has surprised plenty of players besides you because the AI doesn't get level 6 devastator's too often, and it is one of the few ultimate abilities the AI seems to use. As for its weakness, I think the healing stops if the target ship is destroyed (but the target is usually one of your caps), and it has a really long cool down time (at least 3 minutes, maybe longer). I'm not sure if it can be interrupted, but if it can, an Akkan with ion bolt is your best friend.

Anyways, you would have probably been better off going for the carrier, even if the devastator didn't have disintegration because the carrier can heal the whole Vasari fleet and strikecraft. If you see the shield restore buff on a devastator, just switch targets until its done and then you should be able to destroy it in more than enough time before it can use it again.

The Overseer ability is an instant hull boost, and can be done continuously if there are enough of them....it is not uncommon for the AI to have lots of Overseers, and when you focus on a single ship, you can bet every single one of those overseers is going to be adding HP as fast as it can to the target you're hitting...getting a boost of 250 HP every second or so can make it difficult to take out any target...given that the shields were regenerated as well, its clear that the Ultimate ability, disintegration, was being used...however, the Overseers + Repair cloud would have made it extremely difficult to take out that ship until the overseers and skirantra got low on antimatter...

In general, its likely you'll never need more than 4 capital ships unless the game goes on A LONG time....to put things into perspective, one capital ship at lvl 1 does about 50 damage per second...5 Kodiaks (which is 50 fleet supply, the same as a capital ship) do 18 * 5 = 90 damage per second...capital ships don't dish out that much firepower until their higher levels...abilities are what make capital ships valuable, not their firepower...you are better off having 2 or 3 high level capital ships than 6 low level capital ships, and with fewer capital ships, they will level up faster since experience points are distributed amongst all capital ships in the gravity well..

yeah the Kortul Devastator is a good tank battleship, better than the Kol now