The ownership issue actually is two seperate requirements, 'Substancial Ownership' and 'Effective Control'
Substancial Ownership - considered to be the ownership of 50% or more of voting shares of the airline stock. However recently with airline stock becoming traded multinationally and also cross border airline mergers the benchmark is revised and more flexable to allow for example 60% of the stock to be in the hands of foreign shareholders (individuals or corporate) as long as 40% are 'substancially owned' by nationals who represent the most important owners.
Effective Control - has nothing to do with numbers or stock but rather who effectively controls (runs) the airline i.e. the right to hire and fire, to set corporate goals, make strategic decisions. The US Securities Exchange Act of 1934 defines control as 'means the possession, direct or indirect, of the power to direct or to cause the direction of the management and policies of a person, whether through the ownership of voting securities, by contract or otherwise'.
The US DOT sets a 'control test' which looks at financial control through equity ownership and then at control through personal relationships. Satisfaction of the US statutory requirements for 'Substancial Ownership' is not sufficient to determine an airline is a US airline - the airline must also be deemed to be 'Effectively Controlled' by US citizens.
The EU has defined a definition of 'effective control' under Regulation 2407/92 of 23 July 1992 which is similar to the US direction.