Wonder how to they handle branding issues, though? For example infringement? They can’t possibly have all entities go after the offenders, they must coordinate that somehow? Not to mention logo or other branding changes.
Usually one company will own the trademarks and license them to the other, so only one of the companies is responsible for managing the IP. E.g. the Rolls-Royce IP is owned by Rolls-Royce (the aerospace company) and licensed to the company that builds Rolls-Royce-branded cars (currently BMW). The contracts probably stipulate whether and how the spin-off has to handle a logo redesign or whatever else.
If this blows your mind, have a look at how many different companies make and sell products under the Philips brand some time :-)