I can't find any official ruling about this.
I'll use the example of Fog Cloud on the Wild Magic Surge Table (PHB pg. 104) as an example.
The Wild Magic entry reads:
You cast fog cloud centered on yourself.
The spell Fog Cloud (PHB pg. 243) is a concentration spell, lasting for up to an hour.
The rules for concentration (PHB pp. 203-204) state:
Some spells require you to maintain concentration in order to keep their magic active. If you lose concentration, such a spell ends. If a spell must be maintained with concentration, that fact appears in its Duration entry, and the spell specifies how long you can concentrate on it. You can end concentration at any time (no action required).
Normal activity, such as moving and attacking, doesn't interfere with concentration. The following factors can break concentration:
- Casting another spell that requires concentration. You lose concentration on a spell if you cast another spell that requires concentration. You can't concentrate on two spells at once.
- Taking damage. whenever you take damage while you are concentrating on a spell, you must make a Constitution saving throw to maintain your concentration. The DC equals 10 or half the damage you take, whichever number is higher. If you take damage from multiple sources, such as an arrow and a dragon's breath, you make a separate saving throw for each source of damage.
- Being incapacitated or killed. You lose concentration on a spell if you are incapacitated or if you die.
The DM might also decide that certain environmental phenomena, such as a wave crashing over you while you're on a storm-tossed ship, require you to succeed on a DC 10 Constitution saving throw to maintain concentration on a spell.
So, does a spell such as Fog Cloud cast as a result of a roll on the Wild Magic Surge table require concentration? Can the PC that cast it cancel the concentration and the spell effect at will, as with a usual concentration spell? Upon casting, does it cancel any current concentration spells the caster has active? Or does having the level of control over a Wild Magic spell where you can cancel the effect defy the point of the class?