what is the grammatical structure of, he used to have a lot of girlfrinds ut now he has none

There is no need to use the phrase " but now he has none".

 He used to have a lot of girlfriends. It is understood in this sentence that he doesn't have now.

But now he has none is redundant. 

Each of these sentences has two principal clauses, linked by the conjunction, or implied conjunction "but". "Now" is a transitional preposition of time indicating a shift in tense.

The "but" divides the clauses into past perfect - in other words, what once was, but is no longer - and the present, where he finds himself today, without a girlfriend!