It depends.  Some do, some don't.  A simple low tech example is manufacturing, research, and entertainment capitals.  The Entertainment Capital's bonus is spread throughout all colonies (not its adjacent bonus however).  Manufacturing and Research capitals only benefit the individual colonies, so they obviously should be used on focused worlds.

If you want to find out yourself, before building a new building type, go to \Galactic Civilizations III\data\Game\ImprovementDefs.xml

<Improvement>
<InternalName>EntertainmentCapital</InternalName>
<DisplayName>EntertainmentCapital_Name</DisplayName>
<ShortDescription>EntertainmentCapital_ShortDec</ShortDescription>
<Description>EntertainmentCapital_Dec</Description>
<Icon>EntertainmentCapital.png</Icon>
<BuildIcon>EntertainmentCapital_Build.png</BuildIcon>
<ListIcon>EntertainmentCapital_Icon.png</ListIcon>
<ImprovementType>Approval</ImprovementType>
<PlacementType>ApprovalUnique</PlacementType>
<IsPlayerWonder>true</IsPlayerWonder>

<!-- Stats -->

<Stats>
<EffectType>ManufacturingCost</EffectType>
<Scope>Queue</Scope>
<Target>
<TargetType>Improvement</TargetType>
</Target>
<BonusType>Flat</BonusType>
<Value>151</Value>
</Stats>

<Stats>
<EffectType>GoodsAndServices</EffectType>
<Scope>Global</Scope>
<Target>
<TargetType>Colony</TargetType>
</Target>
<BonusType>Multiplier</BonusType>
<Value>0.25</Value>
</Stats>

If an improvement stat element does not have the global scope tag, it will only effect the colony where the building resides.  You can below this in the file, where the other bonuses for the Entertainment Capital is described, there is no global-scope tag.  On the Virtual World improvement, it has global-scope on its in building bonus AND its adjacency bonus(very nice).

<Stats>
<EffectType>InfluencePerTurn</EffectType>
<Target>
<TargetType>Colony</TargetType>
</Target>
<BonusType>Multiplier</BonusType>
<Value>0.25</Value>
</Stats>

<Stats>
<EffectType>Maintenance</EffectType>
<Target>
<TargetType>Improvement</TargetType>
</Target>
<BonusType>Flat</BonusType>
<Value>1.5</Value>
</Stats>

<!-- Triggers -->

<!-- Level Effect Trigers -->

<!-- Level Effect Stats -->

<LevelEffectStats>
<EffectType>GoodsAndServices</EffectType>
<Target>
<TargetType>Colony</TargetType>
</Target>
<BonusType>Flat</BonusType>
<Value>1</Value>
</LevelEffectStats>

<!-- Adjacency Bonuses -->

<NeighborBonuses>
<GiveBonusToNeighborType>Approval</GiveBonusToNeighborType>
<NeighborBonusValue>3</NeighborBonusValue>
</NeighborBonuses>

<NeighborBonuses>
<GiveBonusToNeighborType>Influence</GiveBonusToNeighborType>
<NeighborBonusValue>3</NeighborBonusValue>
</NeighborBonuses>

<NeighborBonuses>
<GiveBonusToNeighborType>Tourism</GiveBonusToNeighborType>
<NeighborBonusValue>3</NeighborBonusValue>
</NeighborBonuses>

<!-- Prerequisites -->

<Prerequ>
<Techs>
<Option>XenoEntertainment</Option>
</Techs>
</Prerequ>

</Improvement>