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From Generation V, female Pokémon with hidden abilities have a 40% chance of passing on the hidden ability to their offspring. Ditto count as male for this purpose.
Cannot use egg moves or gen IV only moves. (this needs to be fixed)
Likewise Togekiss, Mamoswine and Toxicroak cannot use egg moves or gen IV only moves. The former 2 cannot use prevolution moves either.
There seems to be technical difficulties in implementing the ability / move ban though.
At the bottom of this page it says that some Eevee were released as well, and Baton Pass isnt an egg move IIRC, its a pre-evo move so I think it should be legal in fact.
For the record, even if PO hasn't been updated, you can go to any mod to stop a battle that has an illegal Pokemon (giving you the win). If the opponent bitches enough about being forced to lose, they can even kick your opponent for you :D
I go to the TheFourthChaser for all my noob-kicking needs.
As of Black Version 2 and White Version 2, Eevee with their Hidden Ability are available in-game (albeit rarely), so Eevee evolutions may now legally know Egg Moves
...Female Eevees with their hidden ability have been out since May of 2011. PO has been updated with their arrival for ages now; there isn't a problem or a reason to necrobump.