Just use threads and Thread::Queue to distribute the batches:

use strict;
use threads;
use Thread::Queue;
use Net::SMTP;

my @servers = qw(192.168.0.1 192.168.0.2 192.168.0.3);

my @addresses = read_addresses_from_file();

my $queue = Thread::Queue->new();

# Now put 10 addresses into one batch:
while (@addresses) {
    my @batch = splice @addresses, 0, 10;
    $queue->enqueue(\@batch);
};

my @workers = map { my $s = $_; $queue->enqueue(undef); threads->creat
+e( sub {
    my ($ip) = @_;
    my $server = Net::SMTP->new( $ip );

    while (my $batch = $queue->dequeue(1)) {
        print "Sending to $ip: @$batch\n";
        sleep rand 10;
        # ... send using $server ...
    };
    print "Sending to $ip done\n";
}, $s ) } @servers;

for (@workers) {
    $_->join;
};

print "All done.";
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