Unicorn startups have become symbols of entrepreneurial success and fundamental drivers of innovation and wealth creation. This study examines the diffusion process of unicorns across eight countries (the US, China, India, the UK, Germany, France, the Netherlands, and Sweden) and three industries (Fintech, Health, and Transport). The aim of this research is to model and forecast the diffusion of unicorn startups using three-and four-parameter Logistic and Gompertz sigmoid growth models, leveraging data from the Dealroom database. By addressing this research gap, the study seeks to provide valuable information for policymakers and investors regarding the ultimate potential number of unicorns and the time to saturation. The findings indicate that the Gompertz model generates highly optimistic estimates of unicorn saturation levels, while the Logistic model produces more realistic projections for both fitting existing data and forecasting future trends. Specifically, the three-parameter Gompertz model is suited for analyzing unicorn diffusion in China. The three-parameter Logistic model is appropriate for analyzing unicorn diffusion in the USA, the UK, and all studied sectors. Meanwhile, the four-parameter Logistic model is the best model for explaining unicorn diffusion in India, Germany, France, the Netherlands, and Sweden. The results also reveal that India has the highest estimated speed of unicorn diffusion (97%), while the US exhibits the highest saturation level (6,241 unicorns). Sectoral analysis shows that Fintech has the lowest estimated diffusion speed (43.1%), but the highest saturation level (1,630 unicorns). Our forecasting analyses suggest that all selected countries and sectors - except the US and Fintech - are likely to reach unicorn saturation by around 2030. These findings provide critical insights for planning, regulation, policy formulation, and portfolio decision-making.