x5 lost all electrical power.. Help!!

[paul1994]

I was on my home from work with the family in tow and my baby (my 2001 4.4 x5) just completely went dead. all of the lights and everything was dead. Since I had no hazards i had to get out the car and direct traffic around my disabled vehicle until someone came to help me. While waiting for a friend to arrive the lights and everything came back on after sitting there for awhile 10-20 mins . I thought that was weired but i needed to get the family home so I got in the car and started driving home luckily i was less than two miles away. On the way home the car cut out for a second but when i tapped the breaks it seemed to come back.. not sure what happened.

When I got home I decided to check the battery and maybe alternator by looking at the voltage. After the getting the family into the house i went back outside and the truck was totally dead again. SO I manually open the rear trunk to get to the battery. Midway through taking off the bolts the truck came back alive.

I checked the Battery and it was between 12.-12.9 volts

When I started the truck i read 13~ volts.

SO that being said I am not sure where to start to find the problem.
Could the alternator be bad? over heating , voltage regulator?. I just replaced the alternator 02/10, but i was seeing the voltage increase when started.

Any help or ideas would be very much appreciated. Thank you in advanced!