Solution
Since the version AutoCAD Plant 3D 2013 there is a significant change in the handling of tool palettes. When you open your project you will see that the tool palettes shows only two palettes: 'Dynamic pipe spec' and 'Pipe Supports Spec'. Both palettes are dynamically. This is the change in the version 2013.
This means that the content of the palettes will be updated automatically if another spec will be selected (see picture, this will only affect the palette 'Dynamic Pipe Spec') or the content of the spec itself has been changed.

We have here to differ between the palette 'Dynamic Pipe Spec' which is for piping specs and the palette 'Pipe Supports Spec' which is only for the support elements.
Dynamic Pipe Spec
If you switch the spec as you can see in the picture above, the content of the palette will automatically updated to the content of the selected spec. In the spec selection list all the specs are listed which are part of the project. By default they are saved in the folder '<project folder>\Spec Sheets' but you can change this path in the project configuration, node 'Plant 3D DWG Settings - Paths' in the field 'Spec Sheets Directory'.
If you want to modify some elements, you can do this directly in the project spec using the spec editor or you change/add a component in a catalog. Afterewards you add this component to your project spec. Your tool palette will be automatically updated.
Pipe Supports Spec
For the supports a special spec will be used. Its name is 'PipeSupportsSpec'. Like the other specs it is located in the <Plant 3D Content Folder>, but in the subfolder 'CPak Common'. The <Plant 3D Content Folder> is by defaut 'C:\AutoCAD Plant 3D 2013 Content' but can be changed in the spec editor. Like the other specs it will be copied into the folder '<project folder>\Spec Sheets' when a new project will be created in Plant 3D. You can do changes directly in the PipeSupportsSpec of the project using the spec editor. The changes will be directly updated in the tool palettes. If you want to add a new custom support into the support spec, you have to open a special catalog for this. It is the catalog 'SUPPORTS Catalog metric.acat' for metric support or the catalog 'SUPPORTS Catalog.acat' for british supports. Here you can add your custom support component. Afterwards you have to add this component to the PipeSupportsSpec of your project to see the updated tool palette of your project.
Special features 'Add Custom Part' and 'Add Pipe Support'
At the top of the palettes you notice special entries: 'Add Pipe Support' in the palette 'Pipe Supports Spec' and 'Add Custom Part' in the palette 'Dynamic Pipe Spec'. Both have equivalent commands in the ribbon. In the picture you see the equivalent commands for the command 'Add Pipe Support'.

You have the possibility to create here a user-defined component. Be aware that this component will neither be saved in a spec nor as an additional component in the tool palette. Also you have much more possibilities to set properties of a component in a catalog. So a user-defined component which will be created by those two commands are not as precise as a component which was created in a catalog and saved in a spec. Those commands are used for creating a component on-the-fly.
Sharing the tool palettes in a group
Because Plant 3D uses dynamic palettes all people who open the same project have already the same tool palettes because the content of the palettes is coming from the specs which are part of the project.
If you want to sent a project to an extern person, you have to send the whole project but you have nothing specific to do for the tool palettes.
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