Ownership and control documents establish the relationship; contracts, invoices, payroll and financial statements establish that each entity is actually doing business. Both sets are required.
Two distinct evidentiary questions
Hypothetical example: Files often answer the first question thoroughly and the second barely at all. Ownership evidence — share registers, articles, shareholder agreements, resolutions — shows whether the entities stand as parent, branch, subsidiary or affiliate. Activity evidence shows that each is engaged in the regular, systematic and continuous provision of goods or services, which the existence of an agent or a registered address does not establish.
For the Cavan Monaghan parent that means recent financial statements, payroll records, customer contracts and tax filings. For a new U.S. entity it means the premises evidence, the capitalisation, the business plan and whatever activity has already begun.
A closely held company should also expect its corporate record to be read closely, so any discrepancy between the register and the arrangement people describe should be identified and resolved before filing.