  We present a simple model of network growth and solve it by writing down the
dynamic equations for its macroscopic characteristics like the degree
distribution and degree correlations. This allows us to study carefully the
percolation transition using a generating functions theory. The model considers
a network with a fixed number of nodes wherein links are introduced using
degree-dependent linking probabilities $p_k$. To illustrate the techniques and
support our findings using Monte-Carlo simulations, we introduce the exemplary
linking rule $p_k$ proportional to $k^{-\alpha}$, with $\alpha$ between -1 and
plus infinity. This parameter may be used to interpolate between different
regimes. For negative $\alpha$, links are most likely attached to high-degree
nodes. On the other hand, in case $\alpha>0$, nodes with low degrees are
connected and the model asymptotically approaches a process undergoing
explosive percolation.
