  We study a new algorithmic process of graph growth which starts from a single
initial vertex and operates in discrete time-steps, called \emph{slots}. In
every slot, the graph grows via two operations (i) vertex generation and (ii)
edge activation. The process completes at the last slot where a (possibly
empty) subset of the edges of the graph will be removed. Removed edges are
called \emph{excess edges}. The main problem investigated in this paper is:
Given a target graph $G$, we are asked to design an algorithm that outputs such
a process growing $G$, called a \emph{growth schedule}. Additionally, the
algorithm should try to minimize the total number of slots $k$ and of excess
edges $\ell$ used by the process. We provide both positive and negative results
for different values of $k$ and $\ell$, with our main focus being either
schedules with sub-linear number of slots or with zero excess edges.
