The in-game mapmode might help you here, I think. It's a bit hidden, so it's understandable you didn't find it:
Click the
trade zone mapmode button (bottom right):
(Playing as Venice, Dandolo family)
(Optional) Ctrl-left-click on one of the provinces where your
nation has a trade post, to show the
family trade zone mapmode:
Left-click on your capital province - the flashing blue outline indicates all provinces that are in the same trade zone as your capital:
(The various ctrl- and alt-click options are documented in the tooltips when you hover over a province in the relevant mapmode.)
(Amusingly, the Dandolo family starts with an impossible trade post in 1337 - Benevento is landlocked...)
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For trade zone purposes, there are two ways of extending a zone:
- Overland: requires direct land border between two trade post counties owned by the same family
- Oversea: requires "domination" of a sea zone - one family must own more trade posts in that sea zone than any other family. (If it's a draw then no-one dominates.)
Note that the criteria are based on family, not MR. One good reason for choosing not to be elected as Doge is so you can take specific strategic trade posts from other families in your MR (but this only works if you don't already have many more trade posts than them, so it's only useful in the early game).
You can chain these rules. For example, Naupakos-Thebes (plus sufficient other provinces to give you domination of the Ionian and W Aegean) allows you to break into the Aegean (and head for Constantinople) without going around the bottom of Greece. Similarly, Chieti/Aquila-Capua-Rome is great if you want to link Rome to Venice. These land bridges are particularly useful in the early game, when you have a very low trade post limit but want to link up to the super-rich provinces.
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From your screenshot, I can see at least 2 issues:
- The Ionian Sea (W of Greece)
- Two Ragusan trade posts owned by different families, one Venetian trade post, and one Sicilian trade post.
- No single family has more trade posts than any other (they all have one), so there is no single family that controls the Ionian Sea.
- Since your family does not control the Ionian Sea, trade posts on the other side are not "connected to capital".
- Western Cyclades (SE of Greece)
- You have one trade post (Korinthos) and a Ragusan family owns Athenai
- As a result, there is no dominant family in W Cyclades
- Again, your family doesn't control the sea zone, so provinces on the other side are not "connected to capital"