  In this paper, we introduce a class of generalized tracial approximation
${\rm C^*}$-algebras. Let $\mathcal{P}$ be a class of unital ${\rm
C^*}$-algebras which have tracially $\mathcal{Z}$-absorbing (tracial nuclear
dimension at most $n$, $\rm SP$ property, $m$-almost divisible, weakly $(m,
n)$-divisible). Then $A$ has tracially $\mathcal{Z}$-absorbing (tracial nuclear
dimension at most $n$, $\rm SP$ property, weakly $m$-almost divisible, secondly
weakly $(m, n)$-divisible) for any simple unital ${\rm C^*}$-algebra $A$ in the
class of this 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}.
