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This is what I did to get ubuntu up and running:

Install andowook 1.51 with stock kernel (works well with Tux_mind's kernel)
install ES file explorer
go into settings and choose root access, go up to / , and mount /, /sytem (first 3 options)
go into settings and choose show .files (3e option)
install BetterTerminal and let it download the extra files (bussybox).

On your TF prime:
go to tux_mind's blog http://lifeinarootshell.blogspot.it

download this files

3.1.10 kernel for 'any' distro - zImage
root_chooser v6 initrd - root_chooser6.gz (downloads as initrd.gz !)
android stock kernel with kexec patch - android_kernel
android stock initramfs - android_initr

Now on your PC:
Go to http://lifeinarootshell.blogspot.it
Read it! all of it!

Download ubuntu by clicking the big ubuntu logo. this will download: ubuntu-12.04-preinstalled-desktop-armhf+ac100.tar.gz
And: files for any linux distro - root_patch.tar.gz
(And : fastboot.blob under part 4)

Make a new directory ubuntu and place both files in it.
Go in this directory and extract first the ubuntu tarball by typing:
tar -xzf /ubuntu-12.04-preinstalled-desktop-armhf+ac100.tar.gz <enter>

and next extract the root_patch by typing:
tar -xzpf /root_patch.tar.gz <enter>

Format your SD-card as ext4 (you can use Gparted for this)

Copy all the directory's from your ubuntu-directory to the root (/) of your SD-card.
You do not have to copy the tarballs (saves you time)

Unmount your SD-card and eject it, place it in the TF prime.
CAVE: android can't read (or "see") an ext4 SD-card, maybe you get an error "empty card". This is not a problem!

Back on your TF prime
Use ES file explorer and go to the / of your prime and then go to the /data directory
make 3 new directory's:
1) .kernel.d (the dot infront has to be there!)
2) boot
3) mmc

Copy the downloaded file's to /data/boot (android_kernel, android_initr , zImage, initrd.gz)
If the first 3 files have a .txt extension then remove this.

Go to the /data/.kernel.d
and make 2 new files:
1e file: android
and put this in it as plain text:

android
/dev/mmcblk0p8:/boot/android_kernel:/boot/android_initrd

Save the file and delete the android.bak file if it exist

2e file: ubuntu

Copy as plain text:
ubuntu
/dev/mmcblk0p8:/boot/zImage:/boot/initrd.gz
+newroot=/dev/mmcblk1p1:/:/sbin/init

Save it and remove the ubuntu.bak file.

For the last part start up Better terminal.
become root bij typing su <enter> and wait until you get asked if you would give Better Terminal acces. Choose Yes.

Mount the SD-card by typing this:
mount /dev/block/mmcblk1p1 /data/mmc <enter>

Now chroot using this:
chroot /data/mmc /bin/su <enter>
(you now see: root@localhost:/#)
Type in the next lines and replace USER with your name you want to use for loggin in:

groupadd -g 3003 inet <enter>
useradd -d /home/USER -m -s /bin/bash USER <enter>
usermod -aG adm,dip,plugdev,lpadmin,sudo,inet USER <enter>
passwd USER <enter>

You have to give your password twice as you will see.

The solution for the wifi is to add this line to /etc/modules file of your new ubuntu system:
bcm4329 iface_name=wlan0

(You can do this when you started up ubuntu, after changing the file save it and REBOOT the TF prime to take it effect.)

Shutdown android (this will take care of unmounting the SD-card etc..) and boot into fastboot mode.

Follow this from Tux_mind's blog: http://lifeinarootshell.blogspot.it

remember to download the fastboot.blob file first on your computer

step 4
flash kernel_chooser
WARNING: ensure to have created the android config.
first of all you have to choose what method to use for flash the image.
fastboot - it's an open source program that uses an open source protocol
nvflash - it's a closed source program that writes partitions using nvidia custom stuff
personally i prefer fastboot since i can look at his source code if i wish, while when you launch nvflash everything is a secret....
download the image :
fastboot.blob if you choose fastboot
nvflash.LNX if you choose nvflash
here you can find md5sums of the images for doing a check.
now connect you TF201 to your pc and shut it off. if you choose to use fastboot:
take your TF201
keep pressed the volume down button
press the power button until the tablet vibrates
release the volume down key after you see 4 icons
press volume down until the green USB icon being selected
press volume up
go to your pc
open a shell and type fastboot -i 0x0b05 flash boot /path/to/fastboot.blob
you should see a blue bar on your TF201

You are done!
If all went well your TF prime is rebooting and you see the 4 pinguins!

Follow what is on your screen and choose 1 for android and 2 for ubuntu

Good luck and enjoy.

REMEMBER:

Non of the work is mine! I only followed and used the work of others especialy: Tux_mind.

Greetings,

Jos.