It looks like the solution was what is probably the most common solution 
after RTFM and RTFF, namely ITFP (Install the F***** Patch) although the
people responding were kind enough not to put it that way. :-)
Thanks to Gene Loriot (epl@kodak.com)
          Steve Kilbane (steve@cegelecproj.co.uk)
The original patch was 101329 but this patch has been obsoleted by 101318-54
which is available in the collection of recommended patches for Solaris 2.3
named (wait for it) 2.3_Recommended.tar.  After installing the patches, the
problem seems to have gone away.
The patches are available from your local sunsite among others,
        sunsite.unc.edu:/pub/sun-info/sun-patches
        sunsite.sut.ac.jp:/pub/sun-info/sun-us/sun-patches
        sunsite.doc.ic.ac.uk:/sun/sunsite-sun-info/sun-patches
        sunsolve1.sun.com:/pub/patches
To check your present patch level, use the "showrev -p" command.
The original question:
Environment: Sparc 10s and 20s running Solaris 2.3
Symptoms: Every day or two on one of the machines which is the automount source
          for most of the /opt stuff, the automountd process starts growing
          rapidly from a few hundred Kb to 10s or 100s of Mb until the
          automounter locks up and dies.
When I notice things lock up or the process growing, if I do and "autofs stop"
then "autofs start" it cleans up and everything seems normal until next time.
Til Later,
  Kevin
 Kevin O'Donnell                                                   
 Nuclear Medicine Dept.        ' You cannot achieve the impossible 
 Nasu Works, Toshiba Corp.       without attempting the absurd. '  
 kevino@nm.nasu.toshiba.co.jp                                      
 Disclaimer: Any opinions expressed are mine, not Toshiba's.
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