We sell two kinds of 3-way ball valves: one is an L-port, and one is a T-port. This product page shows the T-port valve. The L and the T in the names refer to the hollows in the ball inside the valve and the resulting shape of the open branches. For example, the T-port valves have three hollows in the ball which results in three branches of the valves being open, resembling the shape of a T.
There is a handle on top of the valve which allows you to angle the hollows in different directions, meaning you can open and close whichever branches you need. The design of the T-port means that you are unable to completely shut off the valve, because no matter what way you angle the hollows, there will always be at least two branches open. Both of the valves come with unions on each of the branches so that you can quickly and easily remove the valve and service or replace it, without having to cut your pipe.
People often think, with T-port valves, that when all three branches are open and there is fluid coming in both the right and left branches, that the bottom branch will be expelling 50% of the left flow and 50% of the right flow. In truth, it depends on the pipe system beforehand and the pressures beforehand. If it is the same fluid coming in both branches, then it should split equally. However, if they are different fluids, one might have a slightly different viscosity to the other fluid and it may affect the mixing process in the middle. If the left flow had a slightly higher pressure than the right flow, then almost all the flow will be coming from the left side, because the higher pressure on that side is going to hold back the water on the right. It is possible to adjust the flows, but the problem is, as you shut one port, it's not only closing off the port on that side, it's also closing off the port on another side as well.