Can an Animagus take the form of any animal?

Question

Similar to my old question about what animals a Patronus can be, are there any limits to the animal forms an Animagus can be?

• We know that the animal form can be much smaller than human (cat, rat, beetle) so I don't think size is a factor.

• I'm not aware of any Animagus who transforms into a magical creature (e.g. unicorn or phoenix) so maybe those aren't possible.

Ultimately, what I'd like to know is whether there could be a T-Rex Animagus... (prompted by a funny comment about difficulty with cut/paste while in animal form)

Answer 1

From the existing canon (books, interviews, pottermore till now) the biggest Animagus form we know of was James Potter's stag. (If you go outside canon, JKR claimed - as a jest - that Godric Gryffindor's form was the Giant Squid).

There was never any mention of Animagus form size limitations (clearly you could transform into something bigger as was the case with James, so presumably T-Rex is plausible).

One thing we DO know is that JKR indicated that your Animagus form is NOT something you get to pick and choose and you wouldn't know it before transforming the first time... so you can't simply just pick something "cool".

There was also never any mention of Animagus form being a magical animal. But it's unlikely you will obtain magical powers foreign to you even if you self-Transfigure yourself into the form of a Phoenix or Unicorn.

Wikia lists all known animaguses and their forms.

Answer 2

Yes, but some forms are rarer than others

The animal into which one turns, if an Animagus, seems always to be that which becomes the Patronus.
_{Pottermore - Animagi (behind paywall)}

A Patronus can take on the form of any animal, as evidenced by answers to the following questions:
Can a Patronus take the form of any animal?
What different animal forms have Patronuses taken in Harry Potter canon?