  We consider an urn model with multiple drawing and random time-dependent
addition matrix. The model is very general with respect to previous literature:
the number of sampled balls at each time-step is random, the addition matrix
has general random entries. For the proportion of balls of a given color, we
prove almost sure convergence results and fluctuation theorems (through CLTs in
the sense of stable convergence and of almost sure conditional convergence,
which are stronger than convergence in distribution). Asymptotic confidence
intervals are given for the limit proportion, whose distribution is generally
unknown.
