what happens if i abort transferring files to another computer?

Whatever has already been copied from the source up to the time of interruption will be on the destination. You can look on the destination for that stuff. All the remaining stuff will not have been copied of course. If it was in the process of copying a folder when interrupted then that particular folder is not complete.

You aren't going to break anything by interrupting the copy. You could always elect to delete the already copied stuff on the destination if you don't really want it there.

Were you copying an entire disk? If so you could use DU to erase the entire drive. This is the fastest way to erase an entire drive.

But if you were just dragging selected files and folders to the destination and have stuff on the destination you need to keep, then you cannot erase the entire drive. You have to toss it in the trash. And if it's a large number of files it could take quite a long time.

There are faster ways to delete large numbers of files. But that involves terminal so I won't post it in this context.