Parts are sourced from all over and assembled in back rooms and on kitchen tables usually. There are no "factories" as we know them here. There is a video somewhere if someone can remember the thread it's linked in.
Hum... I'm not so sure it's just made in a kitchen. I'v been working in watches business (quartz fashion watches), and had the opportunity to visit factories in China.
First of all, components are made by different factories. You have suppliers for cases, others suppliers for dials, others for hands, etc... And, of course, suppliers for movements. At the end, you have the assembly of these components which is not so complicated and doesn't need very big equipment.
I'm quite sure that cases are made by suppliers who also make officialy cases for many brands as sub-contractors. These factories have customers (whose business is rep trade) asking for cases and giving them technical specifications for a case. If this case looks exactly like Rolex submariner case, they don't mind. They are just suppling cases, and this il legal (only Rolex engraving at the end is not legal, but nobody cares).
Dials for reps can be made by dial factories. I personnaly visited a dial factory working for the brand I was working for. I saw dials for my company, I also saw people working on dials for other brands. It was mainly fashion brands that are officialy made in China. But I also saw Cartier and Tag Heuer dials...
These are small companies, working in small, old and dirty buildings. But you would be surprised to see the high quality of the products they are able to deliver at the end of the process.
Few pictures I took in a case factory :
Paul