What determines whether or not an animagus can retain their clothes?

I don't think this is covered in canon (and the whole disrepancy is IMHO only from the movies, NOT the books), but it's easy to explain. When you transform, you can take the time to magically "pack" your cloths on your transformed form somehow, unless you:

• Are under duress and rush ("later in the movie, Peter returns to his animal form and leaves his clothes behind - they fall off him before he runs off")

• Don't have any cloth appropriate for the occasion (cause you are a fugitive)

As far as I remember, books don't handle this issue at all, not even a hint. On the few occasions there is a transformation, it is implied that clothes are present in human form and not present in animal form.

That said, I don't think the clothes actually morph with the respective animagus. Instead, they are magically packed and stored (somewhere) at the moment of human-to-animal transformation, and summoned back at the moment of animal-to-human transformation, in the same way that food is summoned from the kitchens to the Great Hall at Hogwarts.

This could have been quite hard to accomplish (in fact, as difficult as what Hermione does with the stuff she packs in her bag), which would be part of the difficulties witches and wizards face when they're in the process of becoming animagi.

To align this idea with what happens in the third movie, remember that Pettigrew did have a wand when he cut his finger and disappeared as a rat, so he actually took his clothes with him (which would support the theory that Black completely finished him off) and kept them until the day Sirius and Remus transformed him back to human form.

The sight of his clothes when he transforms to a rat once again might just be a visual aid to show the proportion (after all, a rat is really small), but it might also be that Pettigrew was in such a hurry (and had not transformed in 13 years) that he forgot to pack his clothes, or intentionally didn't do so, because he would have given Harry time to catch him.

In GoF chapter 37, Hermione makes the following curious comment about animagus Rita Skeeter who is at that time transformed to a bug.

‘[...] Look very closely, and you'll notice the markings around her antennae are exactly like those foul glasses she wears.’

PS chapter 1 gives a similar description of Professor McGonagall, just after she transforms to a human:

a rather severe-looking woman who was wearing square glasses exactly the shape of the markings the cat had had around its eyes.

PoA chapter 6 confirms this:

[McGonagall] transformed herself in front of their eyes into a tabby cat with spectacle markings around her eyes.

This suggests that glasses can morph with together with the wizard, and I think that may apply to other clothes as well.

I would suggest the use of a wand would govern whether or not clothes transform.

Remember that Pettigrew had a wand in his hand and was going to transform using it. He was then disarmed, but still transformed this time leaving his clothes behind.

Perhaps the transformation of clothing can only be achieved with a wand, but the transformation in of and itself can be done without the use of a wand.

Their intent and skill

Generally wizards prefer to have their clothes Transfigure with them, to escape the embarrassment of reappearing naked. However, it is possible to leave clothes behind if one wishes to give the impression of having gone for a bath or something similar. The longer a witch or wizard has been an Animagus, the better they will become at choosing the precise form of their transformations.
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