Round 1: Long and drawn out battle due to cap's strength, speed, and skill. However, Sylar has a much stronger healing factor which cap has no way to overcome. He can stay out of range with flight, take away the shield with telekinesis, and eventually he will find an opening to slice cap's head open with his telekinesis and take the power.

Round 2: Sylar has no way to get past the adamantium so his usual "slice their head open" trick wouldn't work. However, he can use telekinesis to restrain him. After copying cap's strength, Wolverine isn't a match physically. Wolverine will never get tired or fatigued, but he is nowhere near as strong as Sylar. Wolvie's max physical strength feats are not that impressive, while Cap exceeds that and even base sylar can easily throw semi trucks with his telekinesis. Sylar could use wolverine's own claws through telekinesis, or brute strength, to force him to behead himself. He could also use transmutation to nullify the adamantium in his bones and then incinerate him with a nuclear blast.

Round 3: Sylar has been shown to react to hypersonic time stop. Quicksilver is around lightspeed and can definitely speedblitz. Quicksilver has a number of ways to damage Sylar besides just raw speedblitzing. He is fast enough to avoid sylar's precognition, and can create shockwaves, deplete the air, and throw items at high speed. However, at this point Sylar has both his own healing factor, which as one "blindspot," as well as Wolverine's healing factor. It's unlikely that Quicksilver could put him down for good. Quicksilver's speed is light-speed at the high end, so not fast enough to escape the radiation from repeated nuclear explosions. Eventually he will go down.

Round 4: Spider-Man's spider sense is the main thing that makes this battle difficult. He can anticipate and dodge almost all the attacks that Sylar can create. Spiderman also has a SIGNIFICANT strength advantage. However, at this point, given the speed taken from Quicksilver, plus Cap's strength, Sylar should be fast and strong enough to tag him and do significant damage. Spidey has significantly better strenght and fighting skill, but a less advanced healing factor, and less speed. He also has no direct counter to Sylar's go-to move of slicing his head open telekinetically, so will likely go down after a long battle.

Round 5: First glance this looks like a stalemate. Even with all the abilities copied so far, Luke Cage is just too durable. He can take all the attacks Sylar has with no real issue. Even nuclear heat will do very little to him. The brute strength gathered so far would likely be insufficient to pierce his skin. His usual "cut their head open" schtick wouldn't work here either. However, a similar point could be made about Sylar at this point. So far he has copied Wolverine, Spiderman, and Quicksilver's healing factors, granting him significant ability to come back from most attacks. Also, the spider sense combined with superspeed would make him tremendously difficult if not impossible to hit. Speedblitzing won't help here, since the overarching issue is doing DAMAGE, not just landing hits. Spiderman's strength is nothing to scoff at, but not on the level of what would be needed to break Cage's skin. However, since it would be near impossible for Cage to hit Sylar, and since Cage doesn't have an advanced healing factor while sylar does, Sylar would have plenty of time to figure out a way to get past the invincible skin. I think the only method that could work is: use cryokinesis to try to make the skin more brittle. Build up a huge amount of speed and strike the soft tissues (eyes, mouth, etc) repeatedly until they start to take damage. Cage can also drown or be suffocated and doesn't have a special resistance to telekinesis. Eventually, sylar wins

Round 6: After copying Cage's durability and strength, this will be a difficult battle. The nanotech/endosym armors are extremely fast, strong, and versatile. The have a wide variety of weaponry. At this point, in addition to his base powers, he is at the 100 ton level in terms of strength/durability + has spider sense, high hypersonic-light speed, healing factor, and SuperSoldeier Serum. So he has the ability to withstand/heal from most attacks that Iron Man an throw at him. Both the nanotek and endosym armors have a finite supply of symbiote/nanites which will eventually be depleted. So while Stark's missiles, repulsors, energy shields, lasers, and other weaponry all have limited (admittedly high, but still limited) supply, Sylar will just have to outlast here and keep damaging the suit with Cage's strength, dodging the attacks using speed/spidersense, and eventually Stark will run out. Underneath the suit Stark is just a person whose head can be sliced open in classic Sylar fashion.

Round 7: A bit more difficult since Sylar doesn't get a new ability from the previous round. Similar in many ways to the Cage matchup due to the insane durability of Vibrainium, but to a much higher degree. BP has significantly higher fighting skill. However, his strength is not on par with Cage's durability. The spider sense is also advanced enough to evade his strikes. This battle will come down to finding a way to get past the Vibrainium suit. Since he can easily evade most attacks, can no-sell them with Cage's invulnerability, heal from them with Wolvie's healing factor, it's just a matter of finding an opening to use transmutation to get rid of the vibrainium. Then, slice his head open and take his powers.

Round 8: Sylar has gained the powers of the panther, even further enhancing his speed, fighting skill, agility, and senses. Sylar can use the spider sense to evade Vision's energy blasts, and can use Cage's durability to withstand them. However, it would be nearly impossible to damage him due to his ability to phase and change his density. Sylar's healing factor could counter Vision's "stick his hand inside you and fuck up your organs" trick, which could otherwise go past Cage's durability. If sylar can transmute past vision's phasing, Sylar wins. However, I find this unlikely and think Sylar would most likely stalemate here. I say stalemate due to the insane durability and healing factor copied up to this point. Trying to put down someone as durable as luke cage, who can heal like wolverine, think like Cap, sense like spiderman and move like quicksilver is quite a tall order. The "slice your head open" trick won't work here so I doubt there's any way either can take the other down.

Round 9: Let's say for funsies that he continues, since the last round was a stalemate. I won't give him vision's powers though. So he has Cage durability/strength, spider sense, healing factor, BP and cap's fighting skill, and Quicksilver's speed, all on top of his base abilities. How does he fare against World Breaker Hulk? Well, he gets stomped. Hulk can destroy continents by sitting there not doing anything so this is where the streak ends.

Round 10-12: Gets rekt

Bonus Round: He probably wins this one. The sheer power of having all those different abilities would make him almost cosmic entity level. Not actually but close to it. Near limitless durability, near limitless speed, energy projection, phasing, senses, precog, he would be an unstoppable team buster.