  Hypergraphs are structures that can be decomposed or described; in other
words they are recursively countable. Here, we get exact and asymptotic
enumeration results on hypergraphs by means of exponential generating
functions. The number of hypergraph component is bounded, as a generalisation
of Wright inequalities for graphs: the proof is a combinatorial understanding
of the structure by inclusion exclusion. Asymptotic results are obtained,
thanks to generating functions proofs are at the end very easy to read, through
complex analysis by saddle point method. By this way, we characterized:
  - the components with a given number of vertices and of hyperedges by the
expected size of a random hypermatching in these structures.
  - the random hypergraphs (evolving hyperedge by hyperedge) according to the
expected number of hyperedges when the first cycle appears in the evolving
structure.
  This work is an open road to further works on random hypergraphs such as
threshold phenomenon, tools used here seem to be sufficient at first sight.
