In general, you should establish your supervisory committee as soon as possible after you and your supervisor agree on a thesis topic. Even before then, it’s a good idea for your supervisor to consult with prospective committee members about the proposed coursework.
Generally you, as the graduate student, are responsible for establishing your committee in consultation with your supervisor. You should discuss possible choices of committee members with your supervisor, then check UBC Policies and Procedures to ensure that potential members meet all UBC requirements. This decision is often based in part on the research interests and areas of expertise of individual professors. You should consider approaching professors whose expertise and research area overlap somewhat with the thesis topic.
In nearly all cases, you will be asked to contact potential committee members to determine if they are available and interested in serving on your supervisory committee. You can also ask your supervisor to approach a potential committee member on your behalf.