Animagi (Sirus specifically) and wands?

Question

I have 3 questions about animagus transformation and wands

1. Does animagus transformation require the use of a wand?
2. If yes, where does the wand go after the wizard transforms?
3. Again, if 1 is yes, how did Sirius transform into a dog in Azkaban?

Note that 2 and 3 are invalidated if the answer to 1 is no. If so, is it mentioned anywhere in the books, or can be implied by something in the books, that wand use is not required? I don't think Sirius managing to do it in Azkaban can be used as a proof here, as in Book 3 Wormtail needs a wand to change back into a rat

Answer 1

You don’t need a wand to transform.

We know that Sirius was able to transform into his Animagus form while in Azkaban:

“I could transform in my cell… become a dog. Dementors can’t see, you know….”

— Prisoner of Azkaban, chapter 19 (The Servant of Lord Voldemort)

and we know that wands are confiscated before entering Azkaban.

More generally, a human-to-animal Animagus transformation is never depicted as using a wand, and an animal-to-human Animagus must be possible without a wand, because most animals are incapable of wielding a wand.

Answer 2

1. Wand is not required, though it makes thing easier

To return to a human form, visualise your human self as clearly as you can. This should be sufficient, but do not panic if the transformation does not occur immediately. With practice, you will be able to slip in and out of your animal form at will, simply by visualising the creature. Advanced Animagi can transform without wands.
_{Pottermore - Animagi (behind paywall)}

2. The Wand doesn't go anywhere

When your transformation is complete you should find yourself physically comfortable. You are strongly advised to pick up your wand at once, and hide it in a place of safekeeping, where you will be able to find it when you regain a human form.
_{Pottermore - Animagi (behind paywall)}

3. Presumably Sirius was an "Advanced Animagi"

Answer 3

We know that it's not necessary, in general, to use a wand for Animagus transformations, as confirmed by the new information written by JK Rowling for Pottermore:

The legend of the Native American ‘skin walker’ – an evil witch or wizard that can transform into an animal at will – has its basis in fact. A legend grew up around the Native American Animagi, that they had sacrificed close family members to gain their powers of transformation. In fact, the majority of Animagi assumed animal forms to escape persecution or to hunt for the tribe. Such derogatory rumours often originated with No-Maj medicine men, who were sometimes faking magical powers themselves, and fearful of exposure.

The Native American wizarding community was particularly gifted in animal and plant magic, its potions in particular being of a sophistication beyond much that was known in Europe. The most glaring difference between magic practised by Native Americans and the wizards of Europe was the absence of a wand.

The Native American wizards had been doing this for centuries before Sirius was even born, and Rowling specifies that the Wizards were aware of the other peoples/countries for that entire time. It can be inferred they were aware of the ability to transform without wands.

Though European explorers called it ‘the New World’ when they first reached the continent, wizards had known about America long before Muggles (Note: while every nationality has its own term for ‘Muggle,’ the American community uses the slang term No-Maj, short for ‘No Magic’). Various modes of magical travel – brooms and Apparition among them – not to mention visions and premonitions, meant that even far-flung wizarding communities were in contact with each other from the Middle Ages onwards.

The Native American magical community and those of Europe and Africa had known about each other long before the immigration of European No-Majs in the seventeenth century. They were already aware of the many similarities between their communities.