In many upper-division lab courses, instructors implement multiweek student-led projects. During such projects, students may design and carry out experiments, collect and analyze data, document and report their findings, and collaborate closely with peers and mentors. To better understand cognitive, social, and affective aspects of projects, we conducted an exploratory investigation of student ownership of projects. Ownership is a complex construct that refers to, e.g., students' willingness and ability to make strategic decisions about their project. Using data collected through surveys and interviews with students and instructors at five institutions, we developed a preliminary model for student ownership of projects. Our model describes ownership as a relationship between student and project. This relationship is characterized by student interactions with the project during three phases: choice of topic, execution of experiment, and synthesis of results. Herein, we explicate our model and demonstrate that it maps well onto students' and instructors' conceptions of ownership and ideas presented in prior literature.