Possessive pronouns are stand-alone words that both represent the possessed object and the owner. They include, in English: mine, yours, hers and theirs.

Usage is the same as in English. For example: Which car is better?... Yours
and similarly: Whose house is that? Hers.

The genitive is a noun in its own right. It can take all other ending (except é again) and can be applied to all nouns (execpt the plural forms, when you have to use a special plural, see below).

Take care, because in English some possessive modifers are the same as the stand-alone possessive pronouns: his can be used in the context of "that's his car" and That car is his. This page discusses the latter. I will therefore use "hers" to avoid ambiguity, but of course it is gender-irrelevant.

In Hungarian these words are listed below, but don't forget to include the article!

• az enyém mine
• a tied yours
• az övé hers
• a mienk ours
• a tietek yours (pl)
• az övék theirs

• az enyéim (or enyémek) mine
• a tieid yours
• az övéi hers
• a mieink ours
• a tieitek yours (pl) (Check out those three vowels!)
• az övéik (or övéké) theirs

Here are some examples of possessive pronouns at work.

• Ez a kutya az enyém This dog is mine
• Ezek a kutyák az enyéim These dogs are mine
  
  
• Melyiket akarod? Which do you want?
• A tiedet (I want) yours
• Az övéiket (I want) thiers

A good way of remembering that it serves the dual role of possessor and possessed item is to look at the following:

• az én könyvem gives az enyém
• a te könyved gives a tied
• az ő könyve gives az övé
• a mi könyvünk gives a mienk
• a ti könyvetek gives a tietek
• az ő(k)^* könyvük gives az övék

That is, we take the nominative form for the possessor and the external possessive form of the owned object and (kind of) combine them to get these pronouns.

^* Note - az ő(k) könyvük. The correct Hungarian is az ő könyvük but I keep in the plural -k to clarify the point about matching owner and ownee.  See the explanation here: single possession.