Hey!
So from my understanding, they're saying that Mayer Brown is a single partnership (meaning they have the same pot of money and the same salary arrangements) with a huge presence in each of those areas. So, whilst there are other firms that have offices in those areas, either they're not a single partnership in those areas and/or they don't have the presence that Mayer Brown do.
For example, Firm A may have offices in London, NY and HK but London may be part of the Europe arm of the firm, NY is part of the North American arm and HK is part of the Asia-Pacific arm. But, they'll share a common brand. Some examples are Bakers, Dentons, KWM.
Other firms may be integrated in all those areas but might have 1000 lawyers in London, 250 in NY and 50 in HK, etc.
thank you so much for the detailed reply