This novel study explores "AI-giarism," an emergent form of academic dishonesty involving AI and plagiarism, within the higher education context. The objective of this study is to investigate students' perception of adopting generative AI for research and study purposes, and their understanding of traditional plagiarism and their perception of AI-plagiarism. A survey, undertaken by 393 undergraduate and postgraduate students from a variety of disciplines, investigated their perceptions of diverse AI-giarism scenarios. The findings portray a complex landscape of understanding with clear disapproval for direct AI content generation and ambivalent attitudes towards subtler uses of AI. The study introduces a novel instrument to explore conceptualisation of AI-giarism, offering a significant tool for educators and policy-makers. This scale facilitates understanding and discussions around AI-related academic misconduct, contributing to pedagogical design and assessment in an era of AI integration. Moreover, it challenges traditional definitions of academic misconduct, emphasising the need to adapt in response to evolving AI technology. The study provides pivotal insights for academics and policy-makers concerning the integration of AI technology in education.