You asked, "One is open at the bottom and collects hot water from the vent. The density of the hot water is less than the sea in general, so, if the hydrostatic pressure at the bottom is equal to the hydrostatic pressure of the sea, then the pressure in the pipe at the surface will be less than atmospheric, and the hot water will boil and spew, naturally, from the open top. What am I missing here?"

You're missing the throttle valve at the top across which the water flashes to steam in a controlled fashion. That maintains pressure within the pipe, probably higher than the surrounding water pressure.

"A second pipe brings cold water from the bottom to the surface to maximize the temperature difference between the hot water/steam and the condneser temperature. The cold water is more dense than the sea around the pipe. How do you lift the extra weight? You explain it, I'm sure, but I don't see it on your site. You show a pump on the oil platform, but how do you "suck" water up?"

Very astute. The drawing is wrong, (but the verbal description is correct) but I went with it anyway because it seemed easier to understand.

Imagine this large insulated drinking straw extending below the thermocline, open at both the top and the bottom. The top edge would extend several feet above the ocean surface to prevent the pipe's contents from mixing with the surrounding water.

I envision the pump to be floating on that open surface within the "straw", drawing the water only from the surface to the input of the pump. The output of the pump will be carried to the platform 30 m or so above the surface. I'm not actually "sucking up" the water to the platform, but pushing it up.

As water is withdrawn from the surface, obviously the water level inside the "straw" will remain equal with the sea, and that is accomplished because it is refilled at the only point open to the water, with frigid water from below the thermocline. In a very short time the pipe will be filled with only nearly freezing water, and the only pump energy expended will be to pump the volume from the surface to the platform. As long as you recognize that the top of the "straw" is open to the atmosphere, you can see that I'm not actually drawing from the bottom but instead from the surface. That small amount of energy translates to huge gains because of the increased temperature differential.

"The third pipe has to handle the cooled hot water, "waste" minerals, the warmed cooling water, and the condensed steam. Since the density of this warmish waste water will be less than the sea, it will require energy to pump it downward, right? You show a pump in the diagram, but won't it consume a great deal of energy?"

It will require some energy to be consumed in returning that material to the depths, but we are dealing with an abundance of energy at the surface. The warmer waste water can be mixed with surface water to cool it even more, but it will require some work to get it down to the lower levels. I'm not convinced that the waste material has to be returned below the thermocline, and if it does not, then considerably less energy will be required to do the job.