  In this paper we consider a model of spreading information in heterogeneous
systems wherein we have two kinds of objects. Some of them are active and
others are passive. Active objects can, if they possess information, share it
with an encountered passive object. We focus on a particular case such that
active objects communicate independently with randomly chosen passive objects.
Such model is motivated by two real-life scenarios. The first one is a very
dynamic system of mobile devices distributing information among stationary
devices. The second is an architecture wherein clients communicate with several
servers and can leave some information learnt from other servers. The main
question we investigate is how many rounds is needed to deliver the information
to all objects under the assumption that at the beginning exactly one object
has the information?
  In this paper we provide mathematical models of such process and show rigid
and very precise mathematical analysis for some special cases important from
practical point of view. Some mathematical results are quite surprising -- we
find relation of investigated process to both coupon collector's problem as
well as the birthday paradox. Additionally, we present simulations for showing
behaviour for general parameters
