  We introduce multi-centered dilatations of rings, schemes and algebraic
spaces, a basic algebraic concept. Dilatations of schemes endowed with a
structure (e.g. monoid, group or Lie algebra) are in favorable cases schemes
endowed with the same structure. As applications, we use our new formalism to
contribute to the understanding of mono-centered dilatations, to formulate and
deduce some multi-centered congruent isomorphisms and to interpret Rost double
deformation space as both "double-centered" and mono-centered dilatations.
