  We determine the irreducible components of Igusa varieties for Shimura
varieties of Hodge type and use that to compute the irreducible components of
central leaves. In particular, we show that a strong version of the discrete
Hecke orbit conjecture is false in general. Our method combines recent work of
D'Addezio on monodromy groups of compatible local systems with a generalisation
of a method of Hida, using the Honda--Tate theory for Shimura varieties of
Hodge type developed by Kisin--Madapusi Pera--Shin. We also determine the
irreducible components of Newton strata in Shimura varieties of Hodge type by
combining our methods with recent work of Zhou--Zhu.
