How can I control which related components are published when a particular component is published?

What you are experiencing is the default Tridion behavior. This is by design to ensure that when content is changed in a component, the publication will update all instances of that content on the website.

Like other answers, you can change this behavior using Custom Resolver:

 using Tridion.ContentManager;
 using Tridion.ContentManager.CommunicationManagement;
 using Tridion.ContentManager.ContentManagement;
 using Tridion.ContentManager.Publishing;
 using Tridion.ContentManager.Publishing.Resolving;

public class UpdateResolvedItems : IResolver
{
      public void Resolve(
            IdentifiableObject item, 
            ResolveInstruction instruction,
            PublishContext context, 
            Tridion.Collections.ISet<ResolvedItem> resolvedItems)
      {
           foreach (ResolvedItem resolvedItem in resolvedItems)
           {
             // Check resolved items, and remove accordingly
           }
      }
}

resolItems. , , .

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