  We show that an embedding of a fixed 0-dimensional compact space $K$ into the
\v{C}ech--Stone remainder $\omega^*$ as a nowhere dense P-set is the unique
generic limit, a special object in the category consisting of all continuous
maps from $K$ to compact metric spaces.
  Using Fra\"iss\'e theory we get a few well know theorems about
\v{C}ech--Stone remainder.
  We establish the following:
  -- an ultrametric space $K$ of weight $\kappa$ can be uniformly embedded into
$\kappa^\kappa$ as a uniformly nowhere dense subset,
  -- every uniform homeomorphism of uniformly nowhere dense sets in
$\kappa^\kappa$
  can be extended to a uniform auto-homeomorphism of $\kappa^\kappa$,
  -- every uniformly nowhere dense set in $\kappa^\kappa$ is a uniform retract
of $\kappa^\kappa$.
  If we assume that $\kappa$ is a weakly compact cardinal we get the
counterpart of the above result without the uniformity assumption.
