If you split the lines into 2 parts, instead of in as many as the line contains, then you'll keep the entire row. Also, you can assign to a list of scalars, whih is easier to handle than an array.

And for the rest, as wfsp already said: push the data onto the anonymous array which comprise the values of the hash (autovivified, so don't worry about the anonymous array not existing).

while (<REG>) {
    chomp;
    my($key, $data) = split "\t", $_, 2;
    push @{$R{$key}}, $data;
}
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After that it's just a matter of looping through the keys, and print out the contents of the array.

foreach my $key (keys %R) {
    open my $fh, '>', "$key.out" or die "Cannot open file $key.out: $!
+";
    foreach my $row (@{$R{$key}}) {
        print $fh "$key\t$row\n";
    }
}
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