1. The document discusses different definitions of fast growth firms and their implications. It finds that employment-based and productivity-based definitions capture different populations with different economic contributions. 2. It analyzes the regional and industry spillover effects of fast growth firms on other firms' employment growth and productivity growth. It finds both positive and negative externalities depending on the industry, region, and firm characteristics. 3. Geographic externalities, including the concentration of fast growth firms within postcodes and their "gravity force", mirror the findings for industry externalities - negative impacts on employment but positive impacts on productivity.