I wasn't able to find this anywhere in the rules. If a master Kobold is completely surrounded at the beginning of the round, does it still spawn?

I've always allowed them to spawn, following the same basic rules as other monster spawns.

From the Shadow Rune Quest Guide:

Quote

Monster figures may be placed anywhere on the tile or tiles indicated in the setup instructions, provided that those spaces are empty. If there is not enough room on the map tile for all the monsters in the group to be placed, excess monsters may be placed in the closest available empty spaces.

17 hours ago, Charmy said:

I've always allowed them to spawn, following the same basic rules as other monster spawns.

From the Shadow Rune Quest Guide:

Is the same true for Call of the Ravens? The wording is identical.

Yeah. I don't think you're ever supposed to disallow a spawn because of insufficient room unless it explicitly says so. Just spawn as close as possible.

yes, I would say the same