xmichikox;164159 wrote1. When does the computer write over them? When the HD is full otherwise?
Whenever the OS requires the space. It depends on the file system you have. FAT32 tries to write consecutively in the hard disk, so if you delete an existing file, you are creating a "gap" inside the data. However, Windows won't write there until it has a file that fits that gap (if you deleted a 128kb text file, and copy a 3mb file to your hard drive, it won't fit there so it won't overwrite the text file. However, if you download a 16kb mail, it will use the gap left by the previous text file).
Other file systems (like Linux' EXT2/3) choose gaps randomly, so the contents may be overwritten just after you deleted it, or whenever the hard disk is filled.
xmichikox;164159 wrote2.Do these files just sit there and take up space?
Well, there is "data" in the sectors in the hard drive, but since the operative system can write there anywhere, they are not "taking up space".
However, since every bit can be 1 or 0, even if you write 0 to every single bit in the hard disk, you will be "taking up space" with 0's everywhere...
xmichikox;164159 wrote3. If yes to both of the above, can you just permanently delete them? I know you can permanently delete files, but I was wondering if that becomes impossible after they've already been "recycled."
Permanently deleting them means setting every bit used by the file to 0. There are programs that do that, whenever you delete something it overwrites the file with 0's or trash so that the file cannot be recovered. However, I think you have the wrong concept about the hard disk. It is not that things "take up space", the space is just there. Imagine the hard drive has 10 bytes, and it looks like (a) 0000000000. You create a file with 1, and so the hard drive looks like (b) 1000000000. Then you delete the file, and your hard drive can either have (c) 1000000000 (however that 1 there can be overwritten anytime since the file is already deleted) or (d) 0000000000. However, note that for the operative system it is the same, it doesn't care about "what" is in the bit it is going to write, only if it can write to it or not. In (a) the computer has 10 slots to write to. In (b) it has only 9, because the first one is being used by a file. In (c) after deleting the file you have 10 slots to write to, even though the first one is occupied by 1 at this moment... the OS doesn't care about whether there is 1 or 0 there, just if it can write there.