"Dale, While the PH is pure AC, it is modified by the ZW circuit board in the controller and the output is not pure sine wave. That is why there are compatibiliy issues with trains that need a pure sine wave."
I assume he is just using the bricks,without the zw transformer controller. The bricks themselves are pure sine wave. If one transformer or controller puts out a chopped wave and the other brand transformer puts out a different type wave they are really never in phase completely as the sine waves will not line up exactly. They may be both positive ,then negative at the same time but potentials will always be a bit different during each cycle. The waves do not transpose exactly.
"Your phasing and parrallel comments seem confusing. If you are going to share a common then transformers should be phased properly. Otherwise, at some cross over that bridges center rail power a large voltage differential will exist."
The original post does not give details of how the layout is wired. If 2 transformers merely share a common the only time phasing is an issue is if somehow the 2 hots are connected as you describe. With careful wiring that can be avoided. The question was can they share a common? and the answer is yes as long as the 2 hots are not connected in any manner.
"Parralleling of transformers to feed a common load continuously is probably not recommended at all due to unregulated power supplies, and much higher fault currents, plus the potential for circulating currents."
I do not recommend paralleling transformers. Lionel does it with 2 bricks putting out 20 amps and I ma not crazy about that idea. 10 amps is enough of a loop IMO.
"Using a common ground and setting up blocks via insulated center rails is not really paralleled transformers operations; other than temporarily as a train cross from one section to the next block. Hence the need to phase transformers. G"
Temporary or permanent you are paralleling the transformers via a 22 gauge wire between rollers of the engine and lighted cars. Not good IMO. If in your house a circuit had a temporary overload condition the electrical system should be designed to handle it. But you should not wire things with the possibility of overloads just because they are temporary or happen only when the planets line up.. Likewise with your train wiring. Roller jumping can be avoided with 2 relays and a transition block. If you are going to parallel 2 transformers temporarily then just parallel them them permanently with proper wiring and breakers rather than doing it with pickup rollers. Not a good arrangement but better than the choice you describe.
Dale H