I played Eve for a few years as part of a corporation in Xetic and then Ascendant Frontier.
So many painful large battles (time dilation got added after I stopped playing), and some wild solo fights. My favourite was the time I got caught solo in a T2 Interceptor, when out scouting. We knew an attack was coming but didn't know where.
I screwed up, and found myself surrounded by 5 enemy player ships, with no possibility of escaping. The only thing going for me was that I was in an inty, and they were in larger ships, so I could outmanouver them. I knew I was done for. If I flew away they'd be able to hit me as the only thing keeping me safe was my radial velocity (I was orbiting the ship faster than their weapons can rotate, but that only really works 1 on 1, to the other ships you're not moving quite as fast)
It was really just about how long I could hold out and making sure I was ready to warp the moment I got podded. I constantly switched orbit between ships, trying to keep them close together so I could maintain high radial velocity, while taking pot shots at them and starting to chip away at armour, and taking glancing shots from them myself. It felt like that fight went on for hours, but it was probably only 5 or so minutes before they finally managed to pod me, and I managed to warp away to freedom. That was probably nearly 20 years ago (I stopped playing maybe late 2007 / early 2008?) and I still remember it vividly. Once I'd got myself to safety I remember just sitting in my seat staring at the screen, as the adrenaline faded.
In one of the wormhole there was an ambush, I got blown up but my buddy managed to lose them, but didn't leave the system. He started talking to them in local chat, and in the end we ended up joining them. We were playing together for a while after, but life ultimately took over for me. My buddy remained for a while. He was a long-haul trucker and would play in his downtime from various truck stops across US and Canada.
NPSI = Not Purple, Shoot It!
Squad up and then move to some objective location and raise hell shooting anything (w/ coordination from squad leader since the idea is to usually pool DPSl) not in the squad.
Players in your own corporation and alliance typically have blue icons, and those you're at war with have red icons- this is based on manually-set "standings". Alliance roams typically have a NBSI policy: Not Blue, Shoot It!, which means you'll be attacking enemies and neutrals.
Bombers Bar!
In a twist of fate, my corp found one of their fleets sitting in wh space waiting on their scouts...
We did the only appropriate thing and bombed them.
I think I giggled for about 3 hours after that, and recalling the story brought a smile to my face.
Time Dilation is the in-game solution for this: the simulation is throttled so the game runs slower for everybody, but doesn't kick people off. Last time I checked, time dilation could go as low as 10% normal time- meaning you can only fire at 10% normal rate, move 10% as fast, etc. It feels like your ship is flying through molasses- it's not fun, but is also more fair for all players.
Alliances that know there will be a big fight can fill out a form with Eve Online to "schedule" the fight so that star system can be migrated to a larger server before the fight.
All the surrounding systems still run at full speed. You can travel large distances and still arrive soon enough to matter in the fight. You can also die, respawn in another system, rejoin the fight, and barely miss anything. The positions in the fight therefore move even slower than time-dilation since ships on both sides are replaced so quickly.
Large groups have a massive advantage over small groups, so alliances are very large and join various alliances-of-alliances. The playerbase is often organized into only 2-3 major coalitions. At some points in history, nearly all the alliances have joined the same coalition, which leads to a strange pax-Romana called the "blue donut" (referring to all the ownable outer-systems being "blue" or allied with each other).
Also, nearly every player in a large fight just follows simple orders. Orbit A and shoot B. There are just a few people calling the shots.
Fights sometimes end just because people are bored, need to sleep, or go to work.