Breaking down activities into smaller deliverables and being able to work with complex dependencies for implementing a true Portfolio Kanban requires easy to use visualization that could scale across different boards. The best approach for the implementation of this scenario is to use the Related Boards View feature which is available on the right side of your current board.
To enable the Related Boards view, use the top right board grid menu and select the Related Boards icon.
Once activated the view will visualize all links from all the existing cards on your board. The information represents in which board and section the linked cards and initiatives are located (i.e. Backlog, Requested, In Progress or Done).
Use the settings icon on the right top to add/remove which related boards should be visualized. Once visualized you could also collapse/expand them inside the view.
Usage and Breakdown
The main purpose of the Related Boards view is to help Managers from the different levels of the company to break down and monitor the execution of their tasks. Would that be a global company initiative or small department project, the same principle is used for setting up the breakdown and the dependencies.
Use the Drag and Drop of a card or initiative from your board to the desired board in the View area to create new cards and set the right link to it.
Drag and Drop directly linked cards inside the Related Boards view and you could create further more dependencies between those components.
A typical use case is breaking down a bigger activity into smaller ones and distributing it across the different teams. After that setting up the sequence, by using Predecessor -> Successor dependencies between the smaller executable tasks.
Monitoring and Filtering
This view is also well used for monitoring of the execution of all related activities as it shows in real time the changes across all the involved teams (boards). To get a more precise view in depth for a single card or an initiative of the current board, use the ctrl+click (selecting) a card. This acts as a filter and shows only the linked items for the selected card.
Note: The links of a card or an initiative that is completed are not shown in the Relative Boards view. The assumption would be that all linked cards should be as well completed (i.e. Located in the done sections of corresponding boards).
Another common use case is to show per "project" at what state it is for each team. Assuming that each board represents the work of a team, the accumulated values shown on top of each related board will then represent the status of the linked cards inside the team's board. This way it's very easy to see what is the progress towards each activity on the upper management level.