  In this paper, we introduce some classes of generalized tracial approximation
${\rm C^*}$-algebras. Consider the class of unital ${\rm C^*}$-algebras which
are tracially $\mathcal{Z}$-absorbing (or have tracial nuclear dimension at
most $n$, or have the property $\rm SP$, or are $m$-almost divisible). Then $A$
is tracially $\mathcal{Z}$-absorbing (respectively, has tracial nuclear
dimension at most $n$, has the property $\rm SP$, is weakly ($n, m$)-almost
divisible) for any simple unital ${\rm C^*}$-algebra $A$ in the corresponding
class of generalized tracial approximation ${\rm C^*}$-algebras. As an
application, let $A$ be an infinite-dimensional unital simple ${\rm
C^*}$-algebra, and let $B$ be a centrally large subalgebra of $A$. If $B$ is
tracially $\mathcal{Z}$-absorbing, then $A$ is tracially
$\mathcal{Z}$-absorbing. This result was obtained by Archey, Buck, and Phillips
in \cite{AJN}.
