One thing I’ve never exactly understood. Why did the victory on Earth in books 53/54 correspond to a total victory over the Yeerk Empire? Most clearly, we never see the Council of 13 get defeated.
This is all kind of background to the main plots of the books, but. What we know happens is something like this.
The yeerks try to take Leera, under Visser One's leadership. They meet andalite resistance, leeran resistance, and Animorph resistance — ultimately they fail (#15 - #18).
V1 gets reassigned to Sleegab Five. Not many details, but it doesn't go well. Doesn't help that Marco has been actively discrediting her within the Empire (#30).
V1 gets rereassigned to Anati (#30).
Toby et al. launch a resistance on the Hork-Bajir Homeworld (#34).
V1 gets tried as a traitor (thanks, Marco) and slated for execution (Visser). V3 becomes V1. This corresponds with the Empire withdrawing from some failed attempts to take other planets.
Eva (after being rescued; thanks Marco) points out that the Yeerk Empire has few territories outside of Earth that aren't being occupied by andalite counter-invasions (#45).
Andalites have occupied Yeerk Homeworld, Taxxon Homeworld, and Sleegab Five, taking them back from Yeerk Empire (#46). Eva knows that the yeerks are trying to convince the andalites that their focus is on Anati, and that their actual focus is on Earth.
Ax persuades Andalite War Council that yeerks are concentrating on Earth, which is a mixed blessing — it gets the andalites to head for Earth, but they plan to annihilate it when they arrive (#46).
Yeerk forces further concentrate on Earth (#51). Eva speculates that they now have 0 other planets, if they've lost Anati.
Jake, Toby, and Eva plan to blow the biggest yeerk pool on Earth to convince the yeerks "Earth isn't worth their time". They know they're making the yeerks some other planet's problem, but need to prevent the andalites from wiping out humanity (#52).
The yeerks are so overcommitted to Earth that blowing the yeerk pool has the opposite effect. New!V1 instead lands the Pool Ship on Earth and throws everything at an open Earth invasion (#53).
Eva, Jake, Arbron, and V17* conspire to both draw andalite forces to Earth and conceal that fact from new!V1. Now all the andalites' and all the yeerks' eggs are in the Earth basket (#53).
Jake corners V1 and forces him to surrender. V17 reveals to the Empire that the andalites are here, and plans to use that chaos to escape with a splinter group. The andalites accept Jake's handing over the Yeerk Empire (#54).
Rachel kills Tom, preventing V17's escape.
Ax and Alloran manage to negotiate Earth remaining independent, even as the andalites take control of the Yeerk Empire.