  The complete classification of classical $r$-matrices generating quantum
deformations of the (3+1)-dimensional (A)dS and Poincar\'e groups such that
their Lorentz sector is a quantum subgroup is presented. It is found that there
exists three classes of such $r$-matrices, one of them being a novel
two-parametric one. The (A)dS and Minkowskian Poisson homogeneous spaces
corresponding to these three deformations are explicitly constructed in both
local and ambient coordinates. Their quantization is performed, thus giving
rise to the associated noncommutative spacetimes, that in the Minkowski case
are naturally expressed in terms of quantum null-plane coordinates, and they
are always defined by homogeneous quadratic algebras. Finally, non-relativistic
and ultra-relativistic limits giving rise to novel Newtonian and Carrollian
noncommutative spacetimes are also presented.
