After the holidays my ISP has always hundreds of e-mails waiting for me. These are forced down Exim's throat in one go. Exim spawns a lot of kids, but is there some limit to the number of processes it creates?

Unless you have changed smtp_accept_queue_per_connection it should spawn only that many processes per connection (default 10). Your ISP may be making many connections, of course. That is limited by smtp_accept_max.

---