How could Picard take control of the fleet so easily?

Question

In the Battle of the Sector 001, when Picard came to Earth to engage Borg after violating his direct order, he had a special coordinate in mind which could blowout the Borg cube and Starfleet had no idea about it.

Then, there's this thing called luck which rolled in the favor of Mankind and Riker was seen saying, "Admiral's ship's been destroyed." After that, Picard wasted no time to broadcast "I am taking command of the fleet." and gave everyone a special coordinate to fire. And, everything went smoothly and quickly. No conflict. No discussion. No thought of conspiracy from Picard (there was a reason why Picard was given orders to stay out of it). How can this happen?

What does protocol say? I don't think Picard was just below the rank of Admiral. Why didn't other seniors object? Specially, when Picard wasn't fit for fighting against the Borg (in the eyes of Starfleet). And, why did everyone follow Picard's order?

Update:
Here’s the Battle of Sector 001 in case you have forgotten:

Answer 1

Citing the event's of Equinox, we know that

"Starfleet Regulation one hundred ninety one, Article fourteen. In a combat situation involving more than one ship, command falls to the vessel with tactical superiority. I looked it up this morning." - Janeway

In First Contact, we're told that the Enterprise-E is the most advanced ship in the fleet. So that would mean that, the Admiral's ship having been destroyed, command falls to Picard simply by being in command of the most powerful ship present.

Picard first took command of the Stargazer in 2333 and was promoted to Captain some time before 2355, and the Battle of Sector 001 took place in 2373: after at least 18 years as Captain, including 9 of them commanding the flagship, he's one of the most senior and most reputable captains around anyway.

Answer 2

1. All the other captains, and definitely not those of lower rank, wouldn't be privy to the rationale behind the orders Picard and the Enterprise were given by the admiralty.

2. While perhaps not the highest ranking captain by seniority, he would still be recognized as the captain of the flagship. In pragmatic terms, this is a very powerful position. (Frankly, I've often questioned why his rank is only captain. Presumably it's mostly so as not to confuse the audience.)

3. He's not requesting, he is ordering.

   PICARD: This is Captain Picard of the Enterprise. I am taking command of the fleet.

   and he is invoking the full weight of the names Picard and Enterprise

4. Possibly, just The fact he's in command of the most powerful and undamaged ship tilts the scales too. Furthermore, As @Tom pointed out, there's later evidence (retcon?) that there's a regulation to this effect.

5. In a battlefield situation, and especially if other captains are concerned with their crippled ships, no one is going to question an experienced captain filling a leadership vacuum. The captains would recognize that it's more important to act as a coordinated force and follow the leadership of any competent leader than to start questioning chain of command.

Answer 3

As far as exact reasons go, I will offer that we do not know Picard's linear number. In the workings of the U.S. Navy at least, all officers are issued a linear number that is used to determine with finality who is the senior officer between two persons of the same rank. When two submarine commanders get into a dispute (these will always be Commanders unless someone died) the person with the lowest linear number has seniority and can choose to keep or defer command authority in joint endeavors. Linear number 1 is reserved for the President of the United States.

So it is quite possible that Picard actually pulled rank on all other units in the engagement. But of course, the real answer is more nuanced.

These ships are commanded by people, and Picard's trustworthiness had been called into question. The final blow had to be dealt by Picard of course, for the fiction. But what happened in-universe was that, at the very moment all was about to be lost, a single voice delivered an answer, and every single commander responded to that voice with absolute trust.

Answer 4

Nobody had time to stop and say "hey, wait a minute… we need to contact Starfleet to get their approval for this change in authority!". The ships were in the middle of a huge battle. They had minutes.

So someone steps up, someone reputable, someone known for having been one of the most famous captains in the fleet for the past several decades, rocking up on the Federation flagship, and with intimate knowledge of the Borg to boot.

And there's no Admiral in sight.

You think anybody's going to question Picard when he jumps into the Admiral's chair and takes command? No. He was showing leadership and everyone went along with it because that's precisely what anyone would have done. In that situation, and at a time like that, you'd have to have had a real beef with Jean-Luc Picard to question his de facto authority, especially as being nitpicky enough to be responsible for leaving the fleet without effective leadership for any protracted period of time was likely to get you, and all of your crew, killed.

Answer 5

Additionally - Riker's statement when they learn they won't be involved in the battle is also indicative:

"Your past experience with the Borg makes you the perfect man to lead this fight"

The other captains (and given the damage to the fleet, it is possible that some captains have died and there are lower ranking officers in command) would know that as well and defer to Picard's experience also.