Thanks for all the responses! This is ace :)
Based on OneByOne's answer (which looked the simplest to me), I added some non-capturing groups (the '(?:' parts - thanks to VonC for introducing me to non-capturing groups!), so the groups that do capture only contain the digits or * character.
^(?:(\d+)\.)?(?:(\d+)\.)?(\*|\d+)$
Many thanks everyone!