wow hartej, that was like a puzzle to me
anyways let me try to understand you better..
You worked for company A, which was bought by company B and was together know as company AB.
Now company AB has sold its entity to company C, but this time you become new hire to company C.
If the above is true, then you need to take one reference letter to company C for this latest tenure, coz you are considered as a new hire here.
However company B (if existing), will have to provide you letter for your services in company AB for the entire term , as company B bought company A and its employees.
This is best i can understand. The idea is, a company can give you reference letter for a period for the complete term, if they acquired the first company as a whole, where the employees were just transitioned and not hired as new hires.
Hope this makes sense. ;D