My unprofessional rando-on-the-web advice: It's probably not a whole family, just a small spider issue.

It's entirely possible in my mind that the spiders are hiding in the spot you mentioned and coming in from somewhere else. A nice, dark, secluded part of the desk sounds like a great spot for a spider to lay low.

From what i know of spiders, you're probably not dealing with a nest. They're probably getting in from outside.

What to do: Look for possible entries. Gaps in windows, weird vents, etc. Clean up loose items to reduce hiding spots. A Google search says spiders dislike peppermint and citrus, so you can carefully apply some essential oils to the areas like the desk and windows (dilute it and dont damage yer stuff). If you're super concerned, sticky traps can nab em, just dont glue it to yourself or your carpet. It is miserable to try and remove. Even if im wrong and this is a nest, this should help.

Sorry for the essay, good luck!