I noticed today that TheDamian posted another way to do it namely:

$anon_scalar_ref = \eval{undef};        # or ...
$anon_scalar_ref = \eval{ $init_val };  # if you prefer anon scalar in
+itialized
[download]

Running:

#!/usr/bin/perl

use strict;
use warnings;

use Devel::Size 'total_size';
use Devel::Peek;

my $a = \"$$";
my $b = \"";
my $c = \do {my $foo};
my $d = \eval{undef};

print total_size($a), "\n";
print total_size($b), "\n";
print total_size($c), "\n";
print total_size($d), "\n";

print "-----\n";

print Dump($a);
print Dump($c);
print Dump($d);
[download]

produced:

29
25
12
12
-----
SV = RV(0x1865b28) at 0x18242d8
  REFCNT = 1
  FLAGS = (PADBUSY,PADMY,ROK)
  RV = 0x224f08
  SV = PV(0x2251fc) at 0x224f08
    REFCNT = 1
    FLAGS = (POK,pPOK)
    PV = 0x1834234 "3484"\0
    CUR = 4
    LEN = 5
SV = RV(0x1865b30) at 0x18242e4
  REFCNT = 1
  FLAGS = (PADBUSY,PADMY,ROK)
  RV = 0x186168c
  SV = NULL(0x0) at 0x186168c
    REFCNT = 2
    FLAGS = (PADBUSY,PADMY)
SV = RV(0x1865b34) at 0x18247a4
  REFCNT = 1
  FLAGS = (PADBUSY,PADMY,ROK)
  RV = 0x224fbc
  SV = NULL(0x0) at 0x224fbc
    REFCNT = 1
    FLAGS = ()
[download]