Most professional mic splitters will have a transformer on one of the two splits, which will effectively block phantom power. This should be one of the very first questions discussed when you and the live sound operator first meet. Decide who gets which leg of the split, and therefore who is responsible for supplying phantom power. Then, be professionals and communicate with each other when you are powering up and powering down, so that the other person has a chance to kill their levels. Do all this and look like a pro.
If, on the other hand, you are not using a proper mic splitter, and are just using some sort of "Y" cord, then all bets are off. You'll likely encounter noise issues, possible problems from a voltage drop with the phantom power (can cause issues with Neumann mics), and just general headaches. In this situation, you'd really be better off taking a line level signal from the live sound mixer's effects inserts or from Aux. sends. Of course, then you have to live with the mixer's pre-amps and the levels set by the FOH guy, which may change when you're not looking.
A far better solution would be for you to buy yourself a few single channel mic splitters, like those made by Rolls, and have those in your kit for those occasions when the live sound rig does not have a proper splitter network. While you're at it, buy yourself the same number of short (2 meter) mic wires to run between each mic and each splitter box. Then you can cause less disruption if the live sound person has already placed mics and run lines. Just unplug the mic (after informing FOH and getting permission) and put that wire in one leg of the splitter, plug the short mic wire between the mic and the box, and then plug your own wire into the other splitter leg and presto, you've inserted yourself without generating a huge hassle, other than having to run your own wires.
This way, you're the pro - you have everything you need to make a recording independently of live sound, you're not causing the live sound guy additional headaches, and everybody's happy.
Frank Lockwood
https://LockwoodARS.com
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