I'm not sure what this technique is called but in my 6 years of decorating I have never been asked to do it.  I am wanting to recreate this cake for my nieces 1ST birthday and need to see a tutorial on the best way to get the fondant to look like this between the layers.... anyone have a link?   http://media-cache-ec0.pinimg.com/originals/94/41/00/944100fec317d76afa3090f68c939e93.jpg

AThe "icing squishing" out? Don't need a tute for that. Just roll out a sausage of fondant, indent it every so often to make the bulgy parts, and adhere to the cake.

Yeah, I don't know that I'd call it a technique, it's just rolling ot a snake of fondant unevenly then stickign it to the cake. Or if you mean the top tier, it's cutting out a wavy piece then sticking it to the cake.

yes thank you...i couldnt tell from the picture if it was just applied on the outside of the pink or if they had actully inserted something between multiple pink layers.  Is there a name for this style cake?

AYep.