A plug here for OpenCorporates, a free database of company information from around the world.
It brings together public record information from many different registers to give you access to information on, at today's count, over 61 million companies.
If you need to follow through and understand chains of shareholdings and directorships, particularly if these cross borders, then the information you need is on their website.
It's an invaluable resource and the people running it have the admirable goal of a more open and transparent world. They deserve our support.