Question

Do they permanently go over? Do they disappear from my Platinum game?

Answer 1

It is pretty much migrating to the new games so yes you do permanently lose your pokemon to the new game.

In short:it is pretty much giving a pokemon to the new games(not trading)

Comments

So it's like the pal park?

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It SHOULD be

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It's very similar to the pal park, but you use the Touch Screen to catch the Pokemon and another DS.

You have to go to Download Play after you talk to the scientist in the Poké Transfer Lab on Route 15.

You cannot trade with any Generation 4 games with Generation 5 games.