Plenty would depend on how the initial invasion of the Inner Sphere was organized, executed and finished. Assuming an ilClan was declared said Clan would be in a position to dictate quite a bit to the other Clans. Removing all other fictional possibilities, I'd say whichever Clan is ilClan could designate a single Clan shepherd for the homeworlds from whatever Clans were either, A. not a part of the invasion, or B. arbitrarily assigned. It's kind of a cop-op answer, but you haven't really provided enough (IMO) information to make a "good call".
So here's the scenario:
All 20 Clans participate in the Invasion.
Invasion goes as planned (bar anything like Tukayyid) and Terra is conquered.
Clan Wolf manages to seize Terra.
ilClan Wolf assigns XXX Clan to shepherd the Homeworlds (but can not - as far as I know - remove said Clan from its Inner Sphere holdings.)
Here's where it gets messy. I don't think the ilClan can just hand stuff over. They'll rule/make policy, but I'm pretty sure reassignment of assets can only be accomplished through Trials since said assets were won in honorable combat. So ilClan Wolf can't stop the other 18 Clans from stripping their enclaves before the hand over, or trialing with the assigned shepherd over ownership.
Although, I might be wrong about that. I'd have to check.