Overseas penalties
From EU3 Wiki
Overseas Penalties apply to colonies AND provinces on your home continent, as long as there is no continuous line of provinces owned by you, from your capital to the province in question. You can see whether it applies to a specific province by hovering over the tax income for a province (in the Province Info panel). If it says "No land connection to capital: -30%", there's no connection.
Land bridges, such as at Gibraltar, allow for a continuous connection. Land bridges are specifically indicated by a symbol in the lower right of the Province Info panel.
The following penalties apply to unconnected provinces for v. 1.3 (thanks to Seelensturm):
overseas = {
local_tax_modifier = -0.3 #30% penalty if overseas.
local_missionary_cost = 0.75 #75% more expensive overseas.
local_spy_defence = -0.05 #5% penalty on defending in overseas.
regiment_recruit_speed = 1.0 #100% longer time to build troops
ship_recruit_speed = 1.0 #100% longer time to build ships
garrison_growth = -0.05 #5% penalty on garrison growth
}
Remember that you can use Regimental Camps or Shipyards to speed production, although ships might just as well be built back home. The RCs help offset how you can't recruit mercs in those provinces.
The Viceroys Idea nullifies the 30% penalty for overseas tax income, but it does not affect the other penalties. Viceroys may trigger the State Bankruptcy event; follow the link for more info.
Also note that if you go full Naval on the Land/Naval DP slider, you get +10% overseas income. Combined with Viceroys, you can actually get 10% more tax income from unconnected provinces than from connected ones!
