comments and improvements are welcomed.

I added some error checking and moved the slice calculation so it is only performed once instead of for every line of the input file:

#!/usr/bin/perl

# Split a tab-delimited text files into n files, repeating
# first column and shuffling columns.
# Julien Textoris

use strict;
use warnings;

#Thanks to Q&A for this !
sub melange_fy {
    my $tab = shift;
    for ( my $i = @$tab; --$i; ) {
        my $j = int rand( $i + 1 );
        next if $i == $j;
        @$tab[ $i, $j ] = @$tab[ $j, $i ];
        }
    }


@ARGV == 2 or die "usage: $0 file N\n\n\tN is the number of new files 
+to create.\n\n";

my ( $file, $n ) = @ARGV;

open IN, '<', $file or die "open '$file' $!";

my @fhs = map {
    open my $out, '>', "$file.$_" or die "open '$file.$_' $!";
    $out;
    } 0 .. $n - 1;


my @ind;

while ( <IN> ) {
    tr/\r\n//d;

    my ( $id, @elmt ) = split /\t/;

    #make the permutation of tab indices only the first time
    if ( $. == 1 ) {
        die "N is too large, N must be less than " . ( @elmt + 1 ) . "
+.\n" if $n > @elmt;
        my @temp = 0 .. $#elmt;
        melange_fy( \@temp );
        @ind = map [ $_ == $n ? @temp : splice @temp, 0, int( @elmt / 
+$n + 0.5 ) ], 1 .. $n;
        }

    for my $i ( 0 .. $#fhs ) {
        print { $fhs[ $i ] } join( "\t", $id, @elmt[ @{ $ind[ $i ] } ]
+ ), "\n";
        }
    }

__END__
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HTH