What could cause my computer to turn on by itself, doesn't do it all the time.
Thank you for your time.

Some things can have a wake up feature that turns your computer on. Something like a network card could do that. There's a feature that is called something like, wake up on LAN, where your network can boot up your computer. You can probably disable this in your BIOS. Not sure what other device could wake it up, or why it is if not something like this.

There is also a wake on phone call.

I would disable all power management features in BIOS first. From there you can also disable the Wake On LAN feature, or better yet, unplug the Wake On LAN cable that connects your NIC (Network Interface Card) to the mobo.

If it's nothing of the above it can also be a fluctuation in your power line. My own computer also starts by itself as soon as the power supply is connected to the power line.

If the voltage goes under a certain level for even a millisecond the computer may thing you just plugged it in and starts.
The easiest solutions would be to switch it off at the power supply on the back of your computer or to use an extension cord with a switch in it that you switch off after you shut down the computer!

BTW:
This also helps with the above mentioned alternatives. No power -> no running computer!!!