#1 morse taper question for new lathe owner

I recently got a great deal on a 12 inch craftsman wood lathe and i read in the OM that the drive center is a #1 Morse taper my lathe's only problem is that it didn't come with a head stock drive center. so after looking at a bunch of different ones online I've seen some listings have a bunch of different sizes what i need to know is are they all the same size on the inside ? i mean as long as i get a drive center that is a # 1 will it fit my lathe ? I'm sure this sounds dumb but honestly i just don't know very much about lathes at all , and I guess i just need some guidance. thank you all for your time.

Any #1 will fit. This is the portion that fits inside the spindles. Any other measurements will be the out side end that drives or supports the wood your turning.

Great! thank you very much sir ! now i can get started with this thing thank you again very much.