What distance (running) is the closest to a boxing match for the cardio-vascular system ?

More similar to repeat 800-1000s. So 3000-10000m type training.

Pro boxers are boxing 10-12 rounds (elite boxers).

Each round last 3 minutes, so in total 36 minutes of boxing, with 1 minute rest in between rounds.

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I would say it's the closest to a 10k fartlek.

Some people will maybe say because of the 1 min rest, it's more like intervals. But I wouldn't really say so because usually each running intervals are ran at a constant pace. Whereas a boxing round is rarely constant pace.

Not a bad analysis.

There are several things at play in boxing that would add complexity to the comparison. One is, you cannot control effort all the time, whereas in running if you mentally give up or take it easy, you are just not going to win the race or have a great workout. In boxing, you lose and possibly get knocked out. There is no glory in second place and it is dangerous.

I kickboxed for 12 years and boxed here and there and practiced some Shotokan and other arts.

I can tell you a fight feels like an 800m race, each round. I know that the arms start dropping even at the end of the first round for many. That minute off is valuable; an oxygen oasis. But some fatigue remains at the start of the next round...so it compounds on you, so the start of subsequent rounds gets tougher and tougher as they go by. That is why as each round goes by, there is typically more and more holding on and using the ropes.

The anaerobic bursts of throwing a few very hard and fast combinations is a 25m all-out sprint in the middle of the 800m race.

It's also more primal. There are nerves. In running you are only going to be slower than others. The entire time in boxing or kickboxing, you are avoiding getting knocked out, while also trying to knock the other guy out. There is a lot of energy used up maintaining and then so much more used when throwing combos or even just getting the footing right and timing the right hand (for orthodox) for the knockout. All that adds to the energy use. You can try throwing the knock out punch 30 times before properly connecting..... that's why you will see fighters stand back with hands up, take a deep breath and collect themselves, teeter on their heels for a moment: they were anaerobic now want to get back into the aerobic zone...so they can go anaerobic again and if no knockout comes, did you look fit for the judges or are you just hanging on for dear life. You need to score points too, but there is an inherent bias to an even-looking fight, if one demonstrated superior fitness, but was unlucky in not connecting.

So it is in-between a glycolytic peaking workout and an 800m race. So sorta like an 800m race with 10, 20, 30m outrageous bursts in there, but obviously with that in mind, there are some slow sections to that 800m race....in the ring.

The difference between shadow boxing in the mirror and hitting the heavy bag is huge. The difference between sparring and hitting the heavy bag is another giant leap - especially if you are sparring with seriousness in advance of a fight. The difference between a fight and sparring can be an even bigger jump in how much effort/energy/oxygen you use and how catabolic a fight can be.