If you're an Animagus (registered or not) does your Patronus always take the same form as your Animagus?

I'm not sure. Logically, it would make sense that they would but Patronus' can change (as tonks showed us). I don't think you can change what your Animagus form is.

I don't think size is relative to how well a Patronus would work; Luna's Patronus is a rabbit, Hermione's is an otter, and Ron's is a Jack Russel terrier (tiny dogs), and Dumbledore's is a Phoenix. None of those are particularly large at all, but they still managed protect their owners just fine.

I've read some theories about this.

People seem to think that the Animagus form is a reflection of parts of your personality that cannot change. After it is established, it can't undergo a change like the Patronus can. Like we see with Tonks, her Patronus changed after she went through a major emotional upheaval. The Animagus form would not, as one person will only ever have one Animagus form.

I like to think that the Animagus form and the Patronus charm are reflections of different parts of your personality (and, thus, are capable of being different from one another). The Animagus would be a personality trait of yourself that you couldn't change unless you tried really hard, such as maybe you're incredibly laid-back. The Patronus, however, is mais based on your emotional personality or what makes you feel safe, such as Harry's father's especulador, veado, despedidas de solteiro or Tonks' amor for Lupin.

And even if you were able to change the personality trait your Animagus form is based off of, the form itself wouldn't change, as it has already been established.

I hope that helps a bit.

Well we don't really know since we haven't seen;Peter's, and Rita's patronus'. It might be true since James' was the same. But i don't know.

Yes, it always corresponds. If you were to become an animagus after learning your patronous, they would be the same. And to answer your other question, the size of your patronous isn't important, but how happy the memories that fuel it are. For example, Hermione's patronous was an otter, a fairly small animal, but it still fended off dementors.