  Several sets of radially propagating null congruence generators are exploited
in order to form 3-dimensional marginally trapped surfaces, referred to as
black hole and cosmological apparent horizons in a Horava universe. Based on
this method, we deal with the characteristics of the 2-dimensional space-like
spheres of symmetry and the peculiarities of having trapping horizons.
Moreover, we apply this method in standard expanding and contracting FLRW
cosmological models of a Horava universe to investigate the conditions under
which the extra parameters of the theory may lead to trapped/anti-trapped
surfaces both in the future and in the past. We also include the cases of
negative time, referred to as the finite past, and discuss the formation of
anti-trapped surfaces inside the cosmological apparent horizons.
