DanDaMan has given me a lot of food for thought about provinceless combat in another thread, and I thought it was worthy of its own thread. I've added some of my own thoughts to it as well.
The Idea
Remove the province system from HoI3's combat system. Provinces may be retained for some administrative functions, but I prefer - and illustrate here - a totally provinceless system.
Why?
This system makes combat more realistic, as you're not fighting over artificial provinces. Instead you fight over key terrain (point objects) on the map - cities, towns, airfields, ports, bridges, etc.
It also allows for more interesting combat, as you get to move your forces without the constraints of abstract and artificial provinces - some of which in HoI2 could be huge and some of which could be tiny.
How it works
1. Radius of action.
In an active, provinceless combat system ground and naval units are represented by point objects on the map - just like towns and cities. The point determines the map location of that unit and is itself determined by the unit's center of mass. The Radius of Action (RoA) is the range of the unit's influence - the limit of the RoA is determined by a percentage of the unit's combat power. If a division has a 20km RoA (20km from the unit's center of mass), that means that 10% of its combat power is effective. Any enemy unit with its center of mass at the 20km mark will be attacked with 10% of the combat power of the division. Likewise, the enemy will attack as well if your division is within their radius of action. As the distance between the two units closes, the combat power of each division increases. At 10km, your division has 50% of its combat power available to it. When the two units are practically on top of each other, each fights with nearly 100% of its combat power.
Aircraft units likewise have a RoA, but theirs is determined by range from their airbase. If a tactical bomber unit has a 500km RoA, they can attack any target within 500km of their airbase.
Naval units are largely treated as other ground units, except their RoAs will tend to be greater and they are restricted to operating at sea.
2. Supply.
Supply is traced via roads and railroads from major friendly cities. If there is no open road/rail link from your division to a friendly city, that division is out of supply.
3. Attacking, defending, and reserve.
When you're attacking, you select a division (or corps or army) and basically click on the map to give it a destination waypoint. Likewise, if you shift+click on the map you can give the unit multiple waypoints. The speed of the advance will be determined by what terrain the unit's center of gravity is located on. If the unit's CoG is on a mountain, it will be slow. If it is on a road, it will be fast.
When defending, instead of selecting waypoints, you create a defensive line. click and drag to create a defensive line. This line will give the defending unit an RoA bonus, so that they can use their entire RoA without range restrictions.
Reserve posture for a division quadruples the RoA of the division, and likewise decreases the overall effectiveness of the unit. It's useful for garrisons and units not in combat.
Illustrations:

Jamaica (picked because it was a good quality map roughly of the style I like).
You can see the road system (red lines) and the important point objects (towns, city, airfield and port).

Here is the radius of action for a tactical bomber unit based at the Jamaican air base. Also in the pic is the info tab of the airbase, which details the size of the base, the value of the air defenses and radar systems of that base as well as what units are based there. If this was a city info tab, it might show IC capacity of the point object, manpower, resources, etc.

Combat.
Enemy division is red and its RoA is shown with the thin red circle around it. The defensive line is the thick red line on the southeast side of it.
The friendly division is blue, with its RoA shown buy a thin blue circle around it. It has attack waypoints that skirt around the red defensive line. Since the friendly division's center of gravity will not touch the defensive line, the defending enemy unit will not receive a defensive bonus.
Also shown is the unit info screen of the friendly division. This is derived from my Build-Your-Own-Division system, and shows the overall capabilities of the division. It also lets you see what kinds of components your division has (tooltips can tell you if your tank battalion is M4A1s or M5s) as well as buttons to disband or upgrade the division (allowing you to swap out battalions if you want).
Also note the leader screen. In this system, the leader is attached to the division like a brigade of its own. If you combine three divisions into a single corps, each division will retain its general and the corps will have its own general on top of that. Also the general will have personality traits (like Vicky) as well as combat traits (like HoI2).
The Idea
Remove the province system from HoI3's combat system. Provinces may be retained for some administrative functions, but I prefer - and illustrate here - a totally provinceless system.
Why?
This system makes combat more realistic, as you're not fighting over artificial provinces. Instead you fight over key terrain (point objects) on the map - cities, towns, airfields, ports, bridges, etc.
It also allows for more interesting combat, as you get to move your forces without the constraints of abstract and artificial provinces - some of which in HoI2 could be huge and some of which could be tiny.
How it works
1. Radius of action.
In an active, provinceless combat system ground and naval units are represented by point objects on the map - just like towns and cities. The point determines the map location of that unit and is itself determined by the unit's center of mass. The Radius of Action (RoA) is the range of the unit's influence - the limit of the RoA is determined by a percentage of the unit's combat power. If a division has a 20km RoA (20km from the unit's center of mass), that means that 10% of its combat power is effective. Any enemy unit with its center of mass at the 20km mark will be attacked with 10% of the combat power of the division. Likewise, the enemy will attack as well if your division is within their radius of action. As the distance between the two units closes, the combat power of each division increases. At 10km, your division has 50% of its combat power available to it. When the two units are practically on top of each other, each fights with nearly 100% of its combat power.
Aircraft units likewise have a RoA, but theirs is determined by range from their airbase. If a tactical bomber unit has a 500km RoA, they can attack any target within 500km of their airbase.
Naval units are largely treated as other ground units, except their RoAs will tend to be greater and they are restricted to operating at sea.
2. Supply.
Supply is traced via roads and railroads from major friendly cities. If there is no open road/rail link from your division to a friendly city, that division is out of supply.
3. Attacking, defending, and reserve.
When you're attacking, you select a division (or corps or army) and basically click on the map to give it a destination waypoint. Likewise, if you shift+click on the map you can give the unit multiple waypoints. The speed of the advance will be determined by what terrain the unit's center of gravity is located on. If the unit's CoG is on a mountain, it will be slow. If it is on a road, it will be fast.
When defending, instead of selecting waypoints, you create a defensive line. click and drag to create a defensive line. This line will give the defending unit an RoA bonus, so that they can use their entire RoA without range restrictions.
Reserve posture for a division quadruples the RoA of the division, and likewise decreases the overall effectiveness of the unit. It's useful for garrisons and units not in combat.
Illustrations:

Jamaica (picked because it was a good quality map roughly of the style I like).
You can see the road system (red lines) and the important point objects (towns, city, airfield and port).

Here is the radius of action for a tactical bomber unit based at the Jamaican air base. Also in the pic is the info tab of the airbase, which details the size of the base, the value of the air defenses and radar systems of that base as well as what units are based there. If this was a city info tab, it might show IC capacity of the point object, manpower, resources, etc.

Combat.
Enemy division is red and its RoA is shown with the thin red circle around it. The defensive line is the thick red line on the southeast side of it.
The friendly division is blue, with its RoA shown buy a thin blue circle around it. It has attack waypoints that skirt around the red defensive line. Since the friendly division's center of gravity will not touch the defensive line, the defending enemy unit will not receive a defensive bonus.
Also shown is the unit info screen of the friendly division. This is derived from my Build-Your-Own-Division system, and shows the overall capabilities of the division. It also lets you see what kinds of components your division has (tooltips can tell you if your tank battalion is M4A1s or M5s) as well as buttons to disband or upgrade the division (allowing you to swap out battalions if you want).
Also note the leader screen. In this system, the leader is attached to the division like a brigade of its own. If you combine three divisions into a single corps, each division will retain its general and the corps will have its own general on top of that. Also the general will have personality traits (like Vicky) as well as combat traits (like HoI2).
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