Christoffel deformation of a measure on the real line consists of multipying
this measure by a squared polynomial having its roots in $\R$. We introduce
Christoffel deformations of discrete orthogonal polynomial ensembles by
considering the Christoffel deformations of the underlying measure, and prove
that this construction extends to more general point processes describing
distribution on partitions: the poissonized Plancherel measure and the
$z$-measures. These deformations contain the theory of Palm measures, and for
example, explicit formulas for the Palm measures of the poissonized Plancherel
measure provide a description of the TASEP with initial wedge condition with
frozen particles. We also obtain new formulas for Palm measures of the
$z$-measures. The extension to the Plancherel measure is obtained via a limit
transition from the Charlier ensemble, while the extension to the $z$-measures
follows from an analytic continuation argument. A limit procedure starting from
the non-degenerate $z$-measures leads to a deformation of the Gamma process
introduced by Borodin and Olshanski.
