In theory, the Italian navy controlled the Mediterranean. That's because it had the largest permanent navy in that sea, of six battleships, and eight cruisers.

There were several reasons why that theoretical control was tenuous at best. The first was that the Italian navy "punched below its weight."

The second was that the British had bases at Gibraltar in the west, and Alexandria (Egypt) in the east. The British had a larger navy overall. So the Mediterranean balance of power depended largely on the comings and goings of the British fleets at these bases.

The final change of control came with operation Torch, when the American navy came in, and the French navy was scuttled at Toulon. With the French out of the picture, and the Americans in, naval control in the Mediterranean passed to Allied hands permanently in November 1942.

Since you did not give a specific timeframe, I will answer for the all timeframe during which the battle for North Africa was active. So I will answer between the end of 1940 and the start of 1943.

Forces in 1940: The Germans have no forces at all in the Mediterranean Sea, since the Free Zone of France controls the coast. Italians have a good position, central in the Mediterranean, both in North in Italy and in South in Lybia. One speech of Mussolini states its will to conquer a new "Roman Empire" with a new Mare Nostrum.

Second, Greece was the target of Mussolini. In this action, the British loans a few air forces to the Greeks, which successfully repelled the offensive on the ground. Some air and naval battles occured along the East Meditteranean, mostly meetings where the Royal Navy had the upper hand with its better tactical coordination and its aircraft carriers.

Explanation:

• Coordination: The Royal Navy was more effective in leaving its officers to their own ideas, and thus the light forces did a good scouting prior to battles. During confrontation, they were more mobile compared to the simple Italian tactics: a group of cruisers in front to find the force of the ennemies, a group of cruisers and battleships to wait for the bait to work, and fire on the approaching ennemy forces
• Aircraft carriers: they were able to scout and to damage the heavy cruisers and battleships of the Italian Navy
• Night fight: some British had the upper hand at night with the help of a radar able to detect ships and give its location with enough precision so that fire by torpedoes or guns could be aimed

The battle of the Matapan Cap is an example of such a fight.

-> Control of sea: Mostly British

In early 1941, the British were in a good position:

• The Compass operation had capture East of Lybia
• Greece stood against Italian attack
• Air forces in the Middle East and Africa were upgrading their capabilities as long as fighters were delivered bu industry and left unused by the end of the Battle of Britain
• The risk of French Vichy fleet came to and end with the battle of Mers El Kebir

Malta was partially reinforced by naval and air forces, and thus the island was able to cut the supplies of Italian forces in Africa.

-> Control of sea: British

But a few problems will arose and soon change the balance of forces:

• First, the Italians were a problem in East Africa and the British used aviation against them
• Second the Vichy forces in Syria were the same problem and the British needed a lot of air and naval forces against them
• Prior to that fight, Rachid Ali, ministry of Irak, lead a riot that the British had to repel with ground and air forces
• Finally, the German forces came into the fight against Greece and thus the British send ground and few air forces there

The Germans also sent forces in Sicily, aiming to bomb Malta: the air attacks were efficient against British air and naval forces on the island, and soon Axis convoys were able to send the Italian and German forces, with Erwin Rommel, in Libya.

Greece was progressively lost and in the meantime, Rommel made the conquest of East Lybia until he is stopped at Tobruk. This leads to new installation of the Luftwaffe and Regia Aeronautica, who both started to attack British naval convoys over the sea (they tried to supply Malta and Tobruk, under siege).

In Greece and later in Creta, the Royal Navy looses important ships while trying to defend the island. Vichy forces are destroyed in Syria, but they were also able to inflict air and naval losses (not speaking of the fight on ground).

So the British are loosing good airbases in Creta and East Lybia and they had lost a lot of ships.

-> Control of sea: Axis in center of Mediterranean sea

During the spring of 1941, the Germans are progressively involving in the theater and multiple fights occur. In summer 1941, the involvement made its effect: Malta is under important pressure of the Axis forces. Multiple air battles occured over the island, but still, with the action of the K force and air attacks, the Axis loose a lotof its supplies between Italy and Lybia.

In the contrary, British are getting supplies by the Atlantic and the Indian ocean, but tactically fail to free Tokrouk with ground attacks. The Axis effort on the sea and the air is increasing. Italians are getting back some units, repaire after the battle of 1940 and the Tarente air raid. Notably the German Kriegsmarine sends U Bootes in the Mediterranean Sea.

From Summer to December 1941, the Allied situation is falling: the Japanese threat, the needs of warships for the Arctic convoys and the Atlantic is bleeding the resources of the Royal Navy. The losses are becoming higher and higher during convoys under air attacks, but also the battleship Barham and the carrier Ark Royal are sunk by German submarines. The K force, operatinf from Malta gets great successes but is decimated in a minefield.

But somehow, the British managed to win on the ground during operation Crusader. December 7th 1941, the Axis retreats from the siege of Tobrouk, but Japan enters the war.

-> Control of the sea: British pass convoys through, and inflict losses from Malta, but the Axis have more freedom of action in the central part. In the air, the Axis is able to massively bomb Malta.

So in the winter and spring of 1942, the Axis is getting the advantage. But still, tactically, the British are getting their head out of the water and they are able to pass convoys despite the combination of naval and air interceptions.

Why is that?

• The German and Italian commanders are not well coordinated
• British naval forces become better in countering the heavy bombing and torpedo aviation (like the Ju 88 and the Sm 79)
• In Malta, Spitfire reinforcements are a good counterpart to the Luftwaffe, which single-engine fighters have not enough loiter time above Malta

-> Control of the sea: still Axis, and British have a harder time to pass convoys

The situation finally turns in favour of the Axis. With multiple bombings, Malta lost its harassment capability in the winter-summer 1942. The 2nd battle of Syrte shows still a tactical difficulty to coordinate, but a capability to harass Malta so high that even if British naval forces avoid Italian cruisers + battleship Littorio to reach the four-merchant convoy, the Axis aviation is able to destroy them in the neighbourhood of La Valette Harbour.

Rommel, well reinforced, is able to fight with success the Allies at Gazala, and he rechas El Alamein. The stall there is giving a chance to the Allies: It is time for Pedestal. This major convoy, the greater ever seen in the Mediterranean Sea, despite heavy losses caused by German and Italian aviation, submarines, minefileds and torpedo boats, passes to Malta with a few merchants. Enough to supply the island. Then carriers send aircrafts to Malta, and with a good coordination, the fighters are able to land, supply and get back in the air before the air raid called by Italian recon airplanes come in. They inflict losses tothe Luftwaffe.

From that time, the capacities of Malta will still increase.

-> Control of the sea: British again

Of course, Torch and the Second battle of El Alamein put the Allies in a better position. But Torch leads also the Germans to invade Tunisia, and their convoys will travel at a greater range from Malta. With little success at the Mareth line and Kasserine, the Axis is able to make the fight continue until 1943. But still, fighters based in Malta inflicts heavy losses to the six engines flying boats. Afrika Korps surrenders.

-> Control of the Mediterranean Sea: definitely Allies

Distance & Air Cover

To add some detail to T.E.D.'s answer, have a look at this (modern) map of the area.

The Allies landed at Casablanca, Oran, and Algiers on 8 November. At the same time the British were finishing the 2nd Battle of El-Alamein and just beginning their drive west.

The Italian Navy was not doing well against the British alone. The arrival of the American fleet and aircraft decidedly tipped the balance of power in the Mediterranean in favor of the Allies. The US brought 3 battleships, 3 heavy cruisers, 5 light cruisers, USS Ranger, and swarms of destroyers and escort carriers to the landings alone. A few weeks later the French Fleet at Toulon is scuttled removing the potential of being seized by Germany.

Air power was a different matter. The British were still thousands of miles away in Egypt. There's 700 km between Oran and Tunis outside the combat radius of many Allied fighter aircraft in 1942. It would take some time for the Americans to build up air bases in their newly liberated (...ish) territory.

The very next day the Germans start air lifting troops into Vichy controlled Tunis with a rapidity that took the Allies by surprise. Tunis is just 200 km from Axis-controlled Sicily. This means Axis convoys and airlifts could have air cover and for a while they had greater numbers of aircraft. The area was also heavily mined. Any Allied air or sea attack would be taking a great risk.

The Allies had tried to prevent the Axis build up with substantial air and sea forces but Tunis and Bizerta were only 190 km (120 mi) from the ports and airfields of western Sicily, 290 km (180 mi) from Palermo and 480 km (300 mi) from Naples, making it very difficult to intercept Axis transports which had the benefit of substantial air cover. From mid-November 1942 to January 1943, 243,000 men and 856,000 long tons (870,000 t) of supplies and equipment arrived in Tunisia by sea and air.

This map also shows the importance of Malta astride the shipping lanes between Italy and North Africa, and why it was so difficult to resupply. By the time of Operation Torch supplies were getting through, and raids from Malta began to cut into Axis shipping to North Africa.

But the weight of Allied numbers finally fell. In April 1943 they began Operation Flax to cut the air supply lines between Tunis and Sicily. They made sweeps attacking air convoys, their staging areas, and air bases whittling down the Italian merchant navy, German transport aircraft, and their escorts.

In May 1943 Operation Retribution ("retribution" for Royal Navy losses at Crete), the Allied naval blockade of Tunis with the order to "Sink, burn and destroy. Let nothing pass". There was no serious naval opposition and Tunis fell shortly after bagging some 230,000 POWs.

See Also

• Military Aviation History - Tunisia: The Forgotten Stalingrad of Africa