  In 2004, Karo\'nski, \L uczak and Thomason proposed $1$-$2$-$3$-conjecture:
For every nice graph $G$ there is an edge weighting function $
w:E(G)\rightarrow\{1,2,3\} $ such that the induced vertex coloring is proper.
After that, the total versions of this conjecture were suggested in the
literature and recently, Kalkowski et al. have generalized this conjecture to
hypergraphs. In this paper, some previously known results on the total versions
are improved. Moreover, an affirmative answer is given to the conjecture for
some well-known families of hypergraphs like complete $n$-partite hypergraphs,
paths, cycles, theta hypergraphs and some geometric planes. Also, these
hypergraphs are characterized based on the corresponding parameter.
