Ultimately, it depends on your team. The Scrum Guide does not specify how refinement happens. However, in scaled Scrum frameworks, such as Nexus and LeSS, Refinement is elevated from an activity to an event and has a little more structure and guidance placed around it. This is to be expected when you have multiple teams coordinating around a single Product Backlog, though.
The teams that I've worked with have wanted to have full-team refinement meetings on the calendar, but other work on refinement happens individually, in small groups, or ad-hoc full team sessions outside of this regularly scheduled refinement session. The regularly scheduled session focuses primarily on estimation, while the work outside of it is about ensuring that the work is clearly captured, makes sense, is appropriately sliced, and is generally ready for the whole team to look at and estimate.
As long as the Product Backlog Items are sufficiently refined and estimated before Sprint Planning and you have enough of Product Backlog Items in this state for the Product Owner to be able to make trade-off decisions about ordering the items, a lot of the hows of refinement are left up to the team.
I would question, though, why you are timeboxing refinement at 10%. The Scrum Guide does not place such a restriction, using 10% as an estimate rather than a firm, fixed window. When I work with teams, time that is significantly lower than 10% for an extended period of time or significantly above 10% for an extended period of time (2-4 Sprints, usually) would raise questions that I may ask about in a retrospective. But this firm timebox is not part of Scrum - I'd want to make sure that adequate refinement is happening. I'd rather spent more than 10% if it makes Sprint Planning and subsequent Sprint executions easier.