Avahi isn't running on the Mac, but on D-Link router. Those entries are from the router, as received by syslogd running on Mac, OS X 10.8.
I'll try to clarify the setup here:
Router, D-Link DIR-825, is running D-Link firmware. It's a system based on Linux kernel. I configure it to log to a remote syslog server, namely a Mac.
Formerly I directed logging to a Mac running Snow Leopard. I had enabled network logging as has been instructed in many posts here: adding NetworkListener to /System/Library/LaunchDaemons/com.apple.syslogd.plist (by uncommenting the lines):
<key>NetworkListener</key>
<dict>
<key>SockServiceName</key>
<string>syslog</string>
<key>SockType</key>
<string>dgram</string>
</dict>
Now I have new Mac Mini running Mountain Lion (OS X 10.8). Above mentioned plist was in binary format, so I converted it to xml first (plutil -convert xml1) and then added the entry. This enabled syslogd to receive log entries from remote system.
The problem: in OS X 10.8 the entries lack host, and thus I can't filter them. Not by means of asl.conf (eg. ? [ = H 192.168.0.1 ] ) nor in Console.app ("Host is equal to 192.168.0.1") nor with syslog (eg. -k Host 192.168.0.1). Even worse, sender is interpreted as host, so if I try "syslog -k Host kernel:" I get kernel messages from the router.
Also, separate files aren't depracated by any means yet. syslog.log and many other files exist, using bsd syslog format. What's written to these is configured in asl.conf, with entries like
# kernel messages get saved in system.log
? [= Sender kernel] file /var/log/system.log mode=0600 gid=80 format=bsd
(above snippet from OS X 10.8 asl.conf as it is, without me having made any changes)
I'm not concerned about having the log entries in specific file, just about being able to filter them in Console.app or with syslog command.