A couple of points:

1. There's a slight bug as is shown in the code below:

   BEGIN {
     *CORE::GLOBAL::ucfirst = sub {
        join ' ', map CORE::ucfirst, split / /, defined $_[0] ? $_[0] : $
   +_;
     }
   }
   
   $_ = "I shouldn't be printing this, but I am anyway.";
   my $var = undef;
   print ucfirst $var;
   [download]

   Perhaps you should be checking for the number of parameters passed instead?

   BEGIN {
     *CORE::GLOBAL::ucfirst = sub {
        join ' ', map CORE::ucfirst, split / /, @_ ? $_[0] : $_;
     }
   }
   [download]

2. The reason I used split ' ' was because the OP used it. Perhaps it's the behavior he wanted. Maybe not? Either way, there are benefits in both approaches.