In most places online I have found that centaurs act as a mount.
Though I can't find text that directly confirms this in Guildmasters' Guide to Ravnica I tend to agree.

However this raises 2 questions.

A mount can act independently and has 3 actions (dodge, dash or disengage action).
So no action for the rider. My player considers his lower body to be the mount while his upper body as the rider. Is there anything RAW or RAI that would allow a centaur to take one of these 3 actions as a free action by considering his lower part his own mount?

One of my players also claimed that a mounted rider can charge by, attack and move on without provoking an opportunity attack.
Is this supported by any of the rules?

In Unearthed Arcana: Centaurs and Minotaurs, Centaurs have the following trait:

Equine Build. […]
Finally, a Medium or smaller creature can ride on your equine back if you allow it. In such a situation, you continue to act independently, not as a controlled mount.

As to answer your question while mounted centaurs are not considered to be controlled mounts and as such they have full access to actions normal characters have though there are no rules stating that centaurs can consider their lower halves to be their mount and i would severely advise against ruling it as such as that would essentially give the centaur twice as many actions as a normal player.

As for your second question your player is wrong. You provoke an attack of oppurtunity and the attacker can choose to attack you

While you’re mounted, you have two options. You can either control the mount or allow it to act independently. Intelligent creatures, such as dragons, act independently.

You can control a mount only if it has been trained to accept a rider. Domesticated horses, donkeys, and similar creatures are assumed to have such training. The initiative of a controlled mount changes to match yours when you mount it. It moves as you direct it, and it has only three action options: Dash, Disengage, and Dodge. A controlled mount can move and act even on the turn that you mount it.

An independent mount retains its place in the initiative order. Bearing a rider puts no restrictions on the actions the mount can take, and it moves and acts as it wishes. It might flee from combat, rush to attack and devour a badly injured foe, or otherwise act against your wishes.

In either case, if the mount provokes an opportunity attack while you’re on it, the attacker can target you or the mount.

You can refer to this question as well as it deals with a similar topic.

One Character, One Creature

My player considers his lower body to be the mount while his upper body as the rider.

The player is fishing for benefits where none are provided by the rules. A centaur is a single creature. He is not his own mount, and there is nothing in the rules to support this "consideration". Ruling in this player's favor gives him more actions than other characters, and throws the action economy balance out the window.

Mounts Are Separate Creatures

Controlling A Mount [...] The initiative of a controlled mount changes to match yours when you mount it. [...]

Initiative [...] If a tie occurs, the DM decides the order among tied DM-controlled creatures, and the players decide the order among their tied characters. [...]

One of the commonly overlooked aspects of mounted combat is the fact that they are two separate creatures with two separate "slots" in the initiative order (even if they're tied). The general rules do not permit interleaving of actions between creatures, even when two creatures have the same initiative score, and there's no special exception for mounted combatants. In other words, they do not go at the same time, they go sequentially. One creature must finish its turn before the other one can go.

A mounted character cannot ride his mount to a location, take his own actions, then ride the mount away. Only after the mount's turn has ended can the rider take a turn. Using the Ready action for "when my mount carries me within range" works, but restricts the rider to a single swing and uses both Action and Reaction.

Mounted Opportunity Attacks

As for provoking opportunity attacks, that's covered in the text, too:

Controlling A Mount [...] In either case, if the mount provokes an opportunity attack while you’re on it, the attacker can target you or the mount. [...]

This is an exception to the normal rule about movement not under your own power.

Opportunity Attacks [...] You also don't provoke an opportunity attack when you teleport or when someone or something moves you without using your movement, action, or reaction. [...]

A lance or the Disengage action serves to mitigate this problem:

• With a lance, the character Readies an attack for when he gets in lance range (it has reach). The mount moves in, the readied action triggers, and the mount moves away. If the mount needs Dash to get there and get far enough away, this is the thing to do. Watch out for creatures with their own reach, of course.




• Disengage still requires the rider to use a Ready action, but as quoted above, if the mount doesn't provoke, the rider doesn't either. This makes the target's reach irrelevant, but does mean the mount can't Dash.