This study based on an extended Unified Theory of Acceptance and Use of Technology 2 (UTAUT2) model, examines factors influencing graduate students' behavioural intention towards adoption and actual use of generative artificial intelligence (GenAI). l. Using a cross-sectional data from 415 graduate students in Ghana, this study employed the partial least squares structural equation modeling (PLS-SEM), importance-performance map analysis (IPMA), and fuzzy-set qualitative comparative analysis (fsQCA) for the analytical approach. The results from the PLS-SEM indicate that performance expectancy, hedonic motivation, facilitating conditions, personal innovativeness, perceived learning opportunities and satisfaction significantly drive graduate students' behavioural intention towards the adoption of GenAI, whereas effort expectancy, social influence, habit, perceived enjoyment, and perceived risk showed no significant effects. Personal innovativeness, satisfaction, and behavioural intention were found to be the significant predictors of actual use behaviour of GenAI, while perceived risk did not. The IPMA highlighted satisfaction as the highest ranked importance factor and personal innovativene ranked as the highest performance factor, while perceived risk was ranked lowest for both importance and performance. The fsQCA further reveals nuanced results indicating that graduate students' low perceived risk combined with high perception of satisfaction, personal innovativeness, learning opportunities predict their intention and actual usage of GenAI. The combined PLS-SEM, IPMA, and fsQCA approach provides robust insights into GenAI adoption among students in higher education, highlighting the interplay of psychosocial perspectives and the need to enhance the functional benefits, user engagement, and institutional support for effective GenAI integration. Thus, this study has practical implications for improving GenAI infrastructure, enhancing user-centered design, fostering curiosity, and strengthening institutional support.