Who owns a mould or tool once it has been paid for?

The party that paid for it, if the purchase documents say so. This is a contractual matter, not an automatic rule, and the default in most factory paperwork is silence. Practically, the tool sits inside the factory's building and the factory controls access, so ownership is only as strong as the writing: state that the tool is the buyer's property, that it is held at the factory on the buyer's behalf, and that it will be released or transferred on request, including photographs and a tool number. Buyers who skip this have discovered that "their" mould could not be moved.