Each page that is allocated for the process (be it a virtual memory page that has the stack on it or the heap) is copied for the forked process to be able to access it.
Actually, it is not copied right at the start, it is set to Copy-on-Write, meaning once one of the processes (parent or child) try to modify a page it is copied so that they will not harm one-another, and still have all the data from the point of fork() accessible to them.
For example, the code pages, those the actual executable was mapped to in memory, are usually read-only and thus are reused among all the forked processes – they will not be copied again, since no one writes there, only read, and so copy-on-write will never be needed.
More information is available here and here.