Do I need a separate probate application in each province if the deceased owned homes in Ontario and Quebec?

Generally, yes — an Ontario grant doesn't automatically give an estate trustee authority over property in another province. Each Canadian province and territory runs its own probate or estate-administration system, so if the deceased owned real property in more than one province, the estate trustee typically needs to deal with each province separately to get authority recognized there.

Quebec adds another layer because it's a civil-law jurisdiction with its own succession rules, quite different from Ontario's common-law system — Ontario law simply doesn't extend there, and Quebec has its own process for recognizing an estate representative's authority over Quebec property. This isn't something an Ontario grant can shortcut; the executor will generally need to take a separate step in Quebec, following Quebec's own procedure, in addition to whatever is done in Ontario for the Ontario property.

Because the exact process, forms, and requirements differ by province, this is a case where getting Ontario counsel to coordinate with a lawyer licensed in Quebec (or the other relevant province) early is worth it — it avoids surprises like a bank or land registry in the other province refusing to recognize authority that only exists on paper in Ontario.