This paper investigates the holographic complexity conjectures in the extended Schwarzschild-de Sitter (SdS) spacetime. The authors consider multiple configurations of the stretched horizons, which are timelike surfaces close to the cosmological and black hole horizons. They analyze the time evolution of different holographic complexity proposals, including complexity=volume (CV), complexity=action (CA), and complexity=anything (CAny). The study shows that when gravitational observables lie only in the cosmological patch, the complexity conjectures exhibit hyperfast growth, except for a class of CAny observables that show linear growth. When restricted to the black hole patch, all complexity conjectures display linear growth, similar to the AdS case. When both the black hole and cosmological regions are probed, codimension-zero proposals are time-independent, while codimension-one proposals can have non-trivial evolution with linear increase at late times. The authors find that codimension-one spacelike surfaces are highly constrained in SdS space, leading to different behaviors of the complexity conjectures depending on the location of the stretched horizon. They also show that the extended SdS background allows for multiple configurations of the stretched horizons, which can be used to study the holographic complexity in different regions of the spacetime. The results suggest that the holographic complexity of a black hole in asymptotically dS space presents different features depending on the location of the stretched horizons, with possible hyperfast, linear, or vanishing growth. The study also highlights the importance of the stretched horizon in the context of static patch holography and the role of the cosmological horizon in encoding information about the temperature and entropy of the universe.This paper investigates the holographic complexity conjectures in the extended Schwarzschild-de Sitter (SdS) spacetime. The authors consider multiple configurations of the stretched horizons, which are timelike surfaces close to the cosmological and black hole horizons. They analyze the time evolution of different holographic complexity proposals, including complexity=volume (CV), complexity=action (CA), and complexity=anything (CAny). The study shows that when gravitational observables lie only in the cosmological patch, the complexity conjectures exhibit hyperfast growth, except for a class of CAny observables that show linear growth. When restricted to the black hole patch, all complexity conjectures display linear growth, similar to the AdS case. When both the black hole and cosmological regions are probed, codimension-zero proposals are time-independent, while codimension-one proposals can have non-trivial evolution with linear increase at late times. The authors find that codimension-one spacelike surfaces are highly constrained in SdS space, leading to different behaviors of the complexity conjectures depending on the location of the stretched horizon. They also show that the extended SdS background allows for multiple configurations of the stretched horizons, which can be used to study the holographic complexity in different regions of the spacetime. The results suggest that the holographic complexity of a black hole in asymptotically dS space presents different features depending on the location of the stretched horizons, with possible hyperfast, linear, or vanishing growth. The study also highlights the importance of the stretched horizon in the context of static patch holography and the role of the cosmological horizon in encoding information about the temperature and entropy of the universe.