You can purchase a full airline, not a problem but if you exceed 50% minus 1 share in the EU or 25% in the US, that airline loses its status as an US or European national (i.e. not an overall but a British or French or Spanish or Italian or..... carrier ) and it implies no more flight rights in the original markets.
If Alitalia should purchase AA and UA , the new entity could maintain only the routes between the US and Italy (US to EU except to Itlay are anyway lost)

If Delta should to purchase Lufthansa and BA could anyway at least fly from the US to any EU country, not only Germany and Spain.