BABtér is not without a predecessor. The animation school of Illyés Academy of Arts started in 2009, and was based in Illyés High School. A process has started, in which Budaörs became a center for animation art education.

The Primanima World Festival of First Animation was established by Tamás Patrovits and Anna Ida Orosz with the help of the city. This event turns Budaörs into an internationally recognised filmcultural scene every October.

On the first day of the 5th Primanima in 2016, BABtér opened its gates, as the first incubator house in Hungary that focuses on animation, as its main activity, and has countless creative artistic courses and cultural happenings. Animation is not just a segment of film production, the word itself contains much more: it is about vivification and encouragement to do conducive and productive things. BABtér targets to accomplish this mission, to open a door wide open to the colorfull world of animation and art.