can anyone plase.. put the map of NY and mark areas which one belongs to each family ?

To be fair from what ive read i think there isnt certain areas what belong to each family, for example, the gambinos could control rackets in the columbos territory and the columbos could countrol rackets in gambino territory. I think thats right im not sure, some other person will come on and tell you exactly the answer..

No area belongs specifically to one family. Each family has a presence in almost every New York borough, but one more than the other.

The Genovese family is the most dominant and have crews in Manhattan, New Jersey, the Bronx, Brooklyn and Queens.

The Gambino family has a large presence in Brooklyn, Manhattan and Staten Island and have also a presence in Queens and New Jersey.

The Lucchese family has a large presence in the Bronx and New Jersey, but has also a presence in Manhattan and Brooklyn.

The Bonanno family has a large presence in Brooklyn and Staten Island, but has also a presence in Queens, Manhattan and New Jersey.

The Colombos have a large presence mainly in Brooklyn.

Sonny going off the line you said "The Genovese family is the most dominant" does this mean, the genovese have the upper hand of the 5?

They are in fact the most powerful of the Five Families and are also the most dominant as it comes to having a presence in all the New York boroughs.

Although it's technically not one of the five boroughs, you can add Long Island as well for all the families to one extent or another. There is a major mob presence there. Also a big presence in Westchester County.

The Bonanno's used to have a big Manhattan (Mulberry street) faction but dont know if they still do.
NJ has alot of Genovese and Lucchese men.