  We provide a unifying entropy functional and an extremization principle for
black holes and black strings in AdS$_4\times S^7$ and AdS$_5\times S^5$ with
arbitrary rotation and generic electric and magnetic charges. This is done by
gluing gravitational blocks, basic building blocks that are directly inspired
by the holomorphic blocks appearing in the factorization of supersymmetric
partition functions in three and four dimensions. We also provide an explicit
realization of the attractor mechanism by identifying the values of the scalar
fields at the horizon with the critical points of the entropy functional. We
give examples based on dyonic rotating black holes with a twist in AdS$_4\times
S^7$, rotating black strings in AdS$_5\times S^5$, dyonic Kerr-Newman black
holes in AdS$_4\times S^7$ and Kerr-Newman black holes in AdS$_5\times S^5$. In
particular, our entropy functional extends existing results by adding rotation
to the twisted black holes in AdS$_4$ and by adding flavor magnetic charges for
the Kerr-Newman black holes in AdS$_4$. We also discuss generalizations to
higher-dimensional black objects.
