Desktop mats or tripod base mats can be asbestos cement or less often asbestos millboard. The softer millboard type didn’t last to long as they were just too soft and also absorbed any spilled liquids. But labs still often have asbestos cement ones in use or tucked away in a corner somewhere.

Piece of compressed asbestos cement used to place oven forks upon.
Common lab set up asbestos cement mat under the bunsen burner and asbestos gauze mat on top of the tripod.
Another asbestos cement sheet piece used to place hot sample holders or crucibles on.

The hardier mats can last decades in a lab slowly shedding asbestos with each use or when collected or thrown into a cupboard. Also like the gauze mats this source of asbestos fibres can end up being in the resipirable zone of the user.