[Android Software Development] palmerx:
Weird. It works on Samsung Galaxy Tab P1000 but it fails on my P1000N (Latin American Version).

This is the log:

---------------------------------------------------------------
Easy rooting toolkit (v1.0)
created by DooMLoRD
using exploit zergRush (Revolutionary Team)
Credits go to all those involved in making this possible!
---------------------------------------------------------------
[*] This script will:
(1) root ur device using zergRush exploit
(2) install Busybox (1.18.4)
(3) install SU files (3.0.5)
[*] Before u begin:
(1) make sure u have installed adb drivers for ur device
(2) enable "USB DEBUGGING"
from (Menu\Settings\Applications\Development)
(3) enable "UNKNOWN SOURCES"
from (Menu\Settings\Applications)
(4) [OPTIONAL] increase screen timeout to 10 minutes
(5) connect USB cable to PHONE and then connect to PC
(6) skip "PC Companion Software" prompt on device
---------------------------------------------------------------
CONFIRM ALL THE ABOVE THEN
Presione una tecla para continuar . . .
--- STARTING ----
--- WAITING FOR DEVICE
--- cleaning
rm failed for *, No such file or directory
--- pushing zergRush"
160 KB/s (23052 bytes in 0.140s)
--- correcting permissions
--- executing zergRush

[**] Zerg rush - Android 2.2/2.3 local root
[**] (C) 2011 Revolutionary. All rights reserved.

[**] Parts of code from Gingerbreak, (C) 2010-2011 The Android Exploid Crew.

[+] Found a GingerBread ! 0x0001b118
[+] Found a Samsung, running Samsung mode
[*] Scooting ...
[*] Sleeping a bit (~40s)...
[*] Waking !
[*] Sending 149 zerglings ...
[+] Zerglings found a way to enter ! 0x10
[+] Overseer found a path ! 0x0001b340
[*] Sleeping a bit (~40s)...
[*] Waking !
[*] Sending 149 zerglings ...
[+] Zerglings caused crash (good news): 0x40219cd4 0x0054
[*] Researching Metabolic Boost ...
[+] Speedlings on the go ! 0xafd2563d 0xafd390ef
[*] Sleeping a bit (~40s)...
[*] Waking !
[*] Popping 24 more zerglings
[*] Sending 173 zerglings ...
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)

[+] Rush did it ! It's a GG, man !
[+] Killing ADB and restarting as root... enjoy!
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
+++ LOG: write failed (errno=14)
--- WAITING FOR DEVICE TO RECONNECT
if it gets stuck over here for a long time then try:
disconnect usb cable and reconnect it
toggle "USB DEBUGGING" (first disable it then enable it)
--- DEVICE FOUND
--- pushing busybox
1638 KB/s (1075144 bytes in 0.640s)
--- correcting permissions
--- remounting /system
--- copying busybox to /system/xbin/
2099+1 records in
2099+1 records out
1075144 bytes transferred in 0.405 secs (2654676 bytes/sec)
--- correcting ownership
--- correcting permissions
--- installing busybox
--- pushing SU binary
198 KB/s (22228 bytes in 0.109s)
--- correcting ownership
--- correcting permissions
--- correcting symlinks
--- pushing Superuser app
failed to copy 'files\Superuser.apk' to '/system/app/./Superuser.apk': No space
left on device
--- cleaning
--- rebooting
ALL DONE!!!
Presione una tecla para continuar . . .

I have plenty of space on my tablet so I don't know if I'm doing something wrong. Any ideas?

Edit: I was indeed out of ROM space. I got rid of some bloatware and tried again, this time it worked perfectly and smoothly. Great work. Thanks so much DooMLoRD. Great work!

You can add Samsung Galaxy Tab P1000N to the list of devices that can be rooted with this method.