How does copy-on-write in fork() handle multiple fork?

If fork is called multiple times from the original parent process, then each of the children and parent will have their pages marked as read-only. When a child process attempts to write data then the page from the parent process is copied to its address space and the copied page is marked as writeable in the child but not in the parent.

If fork is called from the child process and the grand-child attempts to write, the page from the original parent is copied to the first child, and then to the grand child, and all is marked as writeable.

The original page is only marked writeable if it belongs to a single process, which might not be the case if there were multiple forks. The new page is always marked as writeable because it only belongs to the process which attempted to write it.