pic18f flooding serial with zeros when reset
You have a firmare bug.

As spearson said, the PIC's TX pin should have a pullup to avoid glitches at powerup.  If you initialize pins before turning on the UART peripheral, then set the LAT bit high before setting the TRIS bit to 0.  This will keep the line high until the UART is enabled, which should take over at that point.

However, all that only deals with short glitches at startup.  If you are getting sustained characters after the initialization phase, then you have a firmware bug.  What that bug is of course we can't say.  You may have messed up the UART handler, or maybe higher level code is screwing up and constantly sending some byte.

Take a look at the TX line coming out of the PIC with a scope and see what exactly is being sent.  That might give a clue as to where the code is messing up to cause it.  For example, if it looks like a valid framed character, then the UART driver is probably OK and higher level code is bad.  If it looks like a sustained break, then the UART driver is screwed up, or possibly the whole processor is being reset periodically.  The latter could be due to any number of bugs, including inattention to the watchdog timer.

Soapbox:

Instead of throwing up your hands and saying "it's broken", think about what must be happening for you to see the symptom you see.  Keep digging down each layer to get more information.  Putting a scope on the TX line should have been a obvious thing to do before asking anyone for help.

MATLAB is not a good debug tool because you don't know what kind of high level processing it might perform on the serial port.  You want something that shows you low level serial port information.  Once that is working, you can go back to MATLAB to check out passing higher level data.

What have you done to debug your firmware?  Putting the RealIce or any of its poorer cousins on the PIC and stepping thru the code is another obvious thing to do.  This again should have been one of the first things you did before asking anyone for help.

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