As far as I am aware the authorisation code for Win 10 is stored on the motherboard. Essentially once you have installed Win 10 and authenticated it you can re-install it as often as you wish. I have seen one report that says there is a limit of 50 times to the 'as often as you wish' bit but not many will ever come close to that.
And you can replace a hard drive and re-install without any problems. There may be a problem if you have to change a mobo as MS have always considered that a new mobo equalled a new computer but at the same time they have always been fairly reasonable about accepting that mobos can fail.
With Win 10 you can download the ISO from MS burn it to a DVD or USB drive and install from that and authentication will be automatic.