Universal partial order represented by means of oriented trees and other simple graphs

We present several simple representations of universal partially ordered sets and use them for the proof of universality of the class of oriented trees ordered by the graph homomorphisms. This (which we believe to be a surprising result) solves several open problems. It implies for example universality of cubic planar graphs. This is in sharp contrast with representing even groups (and monoids) by automorphisms (and endomorphisms) of a bounded degree and planar graph. Thus universal partial orders (thin categories) are representable by much simpler structures than categories in general.