Does a ranged attack around a corner incur cover penalties?

Question

In case A attacks B with a ranged attack, does B get cover?

I ask because it seems to me that he might not. In the image above I assumed that A has chosen the upper right corner of his square as being the most favorable for his ranged attack.

To determine whether your target has cover from your ranged attack, choose a corner of your square. If any line from this corner to any corner of the target’s square passes through a square or border that blocks line of effect or provides cover, or through a square occupied by a creature, the target has cover (+4 to AC). (PHB p. 150)

The question is whether the line that runs left along the wall provides cover.

But A surely has cover from B's melee attacks.

When making a melee attack against an adjacent target, your target has cover if any line from your square to the target’s square goes through a wall (including a low wall). (PHB p.151)

If you draw lines from the bottom left corner of B's square you certainly cross the walls, so A definetively has cover from B's melee attack.

That would mean that a ranged attacker (A) standing right around the corner of a melee attacker (B) can shoot the melee attacker without penalty and without risking attacks of opportunity. That does not feel right.

On the other hand - if a line running along a wall grants cover you could not shoot down a straight hallway without cover. (See image below) That does not feel right either.

Answer 1

B won't gain cover.

To be "blocked", your line must pass through a border, not just touch it.

I should say the fact borders are mentioned by themselves may realy be missleading. Borders are mentioned specifically because there may be a solid border without a square to belong to. A thing thin enough to be placed between two otherwise clear squares.

Answer 2

Does a ranged attack around a corner incur cover penalties? I ask because it seems to me that he might not.

Correct. If the line from the chosen corner of the ranged attacker's square does not pass through a square or border that blocks line of effect to any corner of the target's square, the target does not receive cover from the attack. In your example, the attacker can choose a corner from which all corners of the target's square can be reached without passing through a square or border that blocks line of effect.

The question is whether the line that runs left along the wall provides cover.

No. No line passes through a square or border that blocks line of effect. A line runs beside the border but does not "pass through" or cross it.

But A surely has cover from B's melee attacks.

Correct.

That would mean that a ranged attacker (A) standing right around the corner of a melee attacker (B) can shoot the melee attacker without penalty and without risking attacks of opportunity. That does not feel right.

Correct. It is a safer position for the ranged attacker.

A ranged attacker can use this strategy to gain an edge; step one square inside an alcove or hallway to attack melee attackers and limit Attacks of Opportunity against the ranged attacker.

On the other hand - if a line running along a wall grants cover you could not shoot down a straight hallway without cover. (See image below) That does not feel right either.

Right. The previous understanding is correct.

Some maps do draw walls a bit thicker than the squares, thus from either ranged attacker's position in your diagrams, the target would have cover, but I wouldn't recommend imposing that cover penalty unless the hallway is intended to be less than 5'.

This does, however point out another modifier. If the hallway is less than 5' but at least 2.5' wide, then strictly speaking, the squeezing penalty (-4) and cover (-4) applies to both positions for both ranged and melee attacks.