Andrew Tate allegedly had some seriously disturbing material on his devices ... including extreme porn depicting sex acts with a horse and an eel ... according to newly filed court docs obtained by TMZ. The allegations are laid out in a massive filing connected to the UK's effort to extradite Tate from the U.S. ... and things get pretty dark. British authorities allege Tate possessed explicit images depicting people having sex with live animals -- specifically a horse and an eel -- along with other extreme porn showing acts likely to cause serious ------- injuries. And that's nowhere near the end of it ... the docs also accuse Tate of making and possessing scores of indecent images and videos of a minor.

This is who Barron Trump idolizes.