Typically the office location influences the type of projects, based on the "specializations" of that office. It's not binary, but the odds are much higher for a certain project that your office has specific expertise.
Staffing process is in reality based on your project track record and the relationships you built inside the firm based on that. If you are an excellent consultant, the same partner will most likely want you on his team for another project as well - as simple as that. On top of that, there is also the "official" staffing process .. which of course won't overrule partner preferences unless you have a different wish and it's realistic for the firm to use you productively on another engagement (e.g. if you want to explore a different industry..).
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