Answer by Lars Trieloff:
Product management as a role is a role of many adjacencies. It interacts with engineering, design, sales, support, professional services, marketing, strategy, and so on.
It is also a role that you can get quite far without. Most companies manage to launch their 1.0 without having an explicit Product Management role, and start to bring in product managers when the dust has settled. Saying that it is a role you can get quite far without is not saying that you can get far without doing the job, which is essential, and thus gets picked up by other parts of the company, in particular the many adjacencies: engineering, design, sales, support, professional services, marketing, strategy, and so on.
This means, by the time a new product manager joins the company (or is promoted from within) the product manager has to work with an existing organizational structure and has to fit the role to the organizational realities. Depending on the strengths of the product manager, she will take more or less of the job responsibilities on and lead in a stronger or weaker way.
It is not generally different in bigger organizations, as bigger organizations grow from smaller organizations or are made up from smaller organizations, which face the same challenges. Some companies have stringently organized product management organizations, but it is not something that can be expected for all large companies.