The Advanced Turf War Mechanics are special additions to the Turf War mechanic in Monster Hunter: World. They are meant to create more unique scenarios in hunts.
What the scenario does is introduce a system that allows a normally weaker monster to win in a Turf War.
For a fanon example if a Cantios got swarmed by four or more Scofisl while it was to engage in a Turf War against a Prime Scofisl, the scenario would play out that the Scofisl all attack the Cantios at once and stop it from attacking their leader by stinging the Cantios with their stingers to Paralyse its limbs. The Prime Scofisl then attacks the Cantios as it tries to fly up to get them off it, and attacks its head then stabs its chest with its stinger to bring it down in defeat.
During this, the monster that is overpowering the stronger monster will have the Turf War name in the box that appears burnt out, and replaced with "Overpower" in orange text, and the box also gains red markings around it to show that the event is happening.
In this scenario, a monster manages to cause another monster to flee the locale. This can either be through a special battle scene or the more dangerous monster scaring the weaker one away. It is mostly done when the weaker monster is near death, but with much weaker monsters they can be scared/attacked off even at full health.
Examples would be a larger monster letting out a large roar that scares a smaller monster away, or violent skirmish that is so bad the loser has no choice but to immediately flee.
Monsters that are the target of a capture quest cannot be the victim of a Repel.
In this scenario, a monster does a special animation that will always result in the death of the other monster. This would often happen when a monster is near death and the monster near death is weaker than the engaging monster.
A clear example for this would be Monoblos reenacting its Monster Hunter 4 Ultimate intro cutscene by impaling a Gendrome on its horn, dragging it through the sands, then throwing it away.
Monsters that are the target of a capture quest cannot be the victim of a Killing Blow.
Basically, another, third monster jumps into a Turf War and messes it up for both of them. This can have a wide variety of consequences. In the most tame version, the Turf War is simply ruined and the two engaged monsters leave the area. However it can go badly for the interrupter, who may end up being hit in the crossfire, attacked and thrown away, or even end up in a Turf War of its own against one of the two.