please tell me the difference: any time, AT any time,anytime?

Question

above three forms confused me. sometimes ANY TIME does not need to put AT ,sometime there is no sapce between ANY an TIME. such as:

You can come in to our office anytime .(no space between ANY and TIME)

You are welcome to use my car any time. (no AT)
He is likely to arrive AT any time.

Come round any time.(no AT)

I'm available AT any time.

Answer 1

'ANY TIME', 'ANYTIME', 'AT ANY TIME' & "AT ANY ONE TIME'

(1) 'any time' - adj+noun combination. You should use it only in positive statements when you are referring to time without saying exactly the time, often because being exact is not possible or does not matter. Example - Tomato is now available at almost any time in the year.
(2) 'anytime' - adverb. It means at a time which is not or does not need to be decided or agreed. Example - Call round to see me anytime. The guests should be here at anytime now.
(3) 'at any time' - phrase. Something that may happen at a time which cannot be stated definitely, but may be very soon. Example - Doctors said the injured man could die at any time.

There is another expression you should know to enrich your vocabulary :
(4) ' at any one time' - phrase. It means at a single point in time or during a single period of time. Example - The library has room for about six hundred readers at any one time.

Answer 2

You used these in perfect sentences so what explanation do you need?
You can see for yourself you cannot interchange these words as they make the sentences mean different things.