  Transient homogeneous nucleation is studied in the limit of large critical
sizes. Starting from pure monomers, three eras of transient nucleation are
characterized in the classic Becker-D\"oring kinetic equations with the
Turnbull-Fisher discrete diffusivity. After an initial stage in which the
number of monomers decreases, many clusters of small size are produced and a
continuous size distribution is created. During the second era, nucleii are
increasing steadily in size in such a way that their distribution appears as a
wave front advancing towards the critical size for steady nucleation. The
nucleation rate at critical size is negligible during this era. After the wave
front reaches critical size, it ignites the creation of supercritical clusters
at a rate that increases monotonically until its steady value is reached.
Analytical formulas for the transient nucleation rate and the time lag are
obtained that improve classical ones and compare very well with direct
numerical solutions. In addition, we propose and solve numerically a modified
Becker-D\"oring model having a discrete diffusivity proportional to the area of
a spherical cluster with $k$ monomers for small $k$ (as in the Turnbull-Fisher
case) and to the cluster radius for large $k$ (as in the case of diffusive
growth of clusters).
