To have is auxiliar when it is alone, without another verbs. If I write: "I have got a cat" this is auxiliar.

While, it is not auxiliar when I accompany "to have" with another verb or a sostantive; for example: "I have breakfast", "You have cut this tree".

Is it right???

Thanks Peachey. So, if I say: "I've got a cat" this is a right structure for the auxiliar;

but, if I say: "I've breakfast soon" it's wrong! I must to say: "I have breakfast soon", because I can't contract that!

I don't know if this is what you are asking for, but ... 

Firstly 'have got' is not an auxiliary verb but a modal one. You have to think that they are two different verbs with 'the same meaning'. 'Have got' is a modal verb and 'have' is not.

Does this answer your question?

If it's an auxiliary verb, there's another verb (the main verb) which is in past participle form.

Also, as an auxiliary verb, "have" can contract (I've, they've, she's, it's....) or take a negative (haven't / hasn't / hadn't). When it's a main verb, it cannot do this.

It's not all that difficult - you can relax. :)