If a company grows organically to have a large market share due to superior product, service, or even luck, don't break them up. But I would say having a dozen serious competitors in a market really prevents a lot of problems. Don't let companies buy each other when it would put the combined company over 10% of the market. Of course this rule can be immediately gamed in many ways but might be able to be done in some decently reasonable way.
Technically humans do own everything. The problem is not being able to find out who owns what because at some point in the chain, there's an entity outside the country or somewhere that has different disclosure rules.
