After doing multiple (say 3) mysql_pconnect() from within
one page, as suspected the number of mysql threads
increases, but only the last connection made is being reused
by subsequent calls to mysql_pconnect from other pages/requests.
This is a bit unconfirmed, since I don't have the time and
resources right now, but tests on a production site (which
has crashed very often the last time) showed that the
following code cut down the number of mysql threads at least
tenfold:

if (!@mysql_select_db ("test")) {
  mysql_pconnect("db","user","pass") or die ("No
DB:".mysql_error());
  mysql_select_db ("test") or die ("database does not exist:
".mysql_error());
}