Title: History of the Southern United States
Content:  Army. Over 1,000 volunteered and served in British uniforms, chiefly in the Ethiopian Regiment. However, they were defeated in the Battle of Great Bridge, and most of them died of disease. The Royal Navy took Dunmore and other officials home in August 1776, and also carried to freedom 300 surviving former slaves. After their defeat at Saratoga in 1777 and the entry of the French into the American Revolutionary War, the British turned their attention to the South. With fewer regular troops at their disposal, the British commanders developed a "southern strategy" that relied heavily on volunteer soldiers and militia from the Loyalist element. Beginning in late December 1778, the British captured Savannah 
Title: Southern theater of the American Revolutionary War
Content:  With the surrender at Yorktown, the full participation of French forces in that battle, and the resulting loss of Cornwallis' army, the British war effort ground to a halt. The sole remaining British army of any size remaining in America was that under Sir Henry Clinton in New York. Clinton, paralyzed by the defeat, made no further action and was replaced by Guy Carleton in 1782. Such a shocking reversal in fortune, coming as it had on the back of a rare naval defeat, served to increase the shift in British popular opinion against the war. The North Ministry collapsed, a peace-oriented government took power, and no further major operation on the American continent occurred for the rest of the war. While Saratoga had started the decline of British fortunes in the Revolution, Yorktown was its death knell.
Title: United Kingdom–United States relations
Content:  British strategy was then refocused on the South, where they expected large numbers of Loyalists would fight alongside the regulars. Far fewer Loyalists took up arms than Britain needed; royal efforts to control the countryside in the South failed. When the British army tried to return to New York, its rescue fleet was turned back by the French Navy and its army was captured by combined French-American forces under General George Washington at the Siege of Yorktown in October 1781. That effectively conceded American success. Opinion in Scotland often favoured the American cause, or criticised the poor performance of the British army.
Title: Southern theater of the American Revolutionary War
Content:  largest surrender of U.S. troops until the American Civil War. With relatively few casualties, Clinton had seized the South's biggest city and seaport, winning perhaps the greatest British victory of the war. This victory left the American military structure in the South in ruins. It was only after Nathanael Greene slipped past Cornwallis after the Battle of Guilford Courthouse in 1781 that the British finally lost this advantage in the South.  The remnants of the southern Continental Army began to withdraw toward North Carolina, but were pursued by Colonel Tarleton, who defeated them at the Battle of Waxhaws on May 29. Historians have debated accounts spread after the battle that Tarleton's forces 
Title: Frederick North, Lord North
Content:  was soon abandoned. Ironically, the war began to turn in Great Britain's favour again in 1782 through naval victories, owing largely to policies adopted by Lord North and the Earl of Sandwich. The British naval victory at the Battle of the Saintes took place after the government's fall. Despite predictions that Gibraltar's fall was imminent, that fortress managed to hold out and was relieved. Great Britain was able to make a much more favourable peace in 1783 than had appeared likely at the time when North had been ousted. In spite of this, North was critical of the terms agreed by the Shelburne government which he felt undervalued the strength of the British negotiating position.
Title: American Revolution
Content:  could still believe in their eventual victory, as British troops inflicted defeats on the Continental forces at the Battle of Camden and the Battle of Guilford Court House. In late 1781, the news of Cornwallis's surrender at the siege of Yorktown reached London; Lord North's parliamentary support ebbed away and he resigned the following year. The King drafted an abdication notice, which was never delivered, finally accepted the defeat in North America, and authorized peace negotiations. The Treaties of Paris, by which Britain recognized the independence of the United States and returned Florida to Spain, were signed in 1782 and 1783 
Title: Anglo-French War (1778–1783)
Content:  sent to assist Lafayette's army in the blockade of Cornwallis. A British fleet sent to confront de Grasse's control of the Chesapeake was defeated by the French on September 5 at the Battle of the Chesapeake, and the Newport fleet delivered the French siege train to complete the allied military arrival. The Siege of Yorktown and following surrender by Cornwallis on October 19 were decisive in ending major hostilities in North America. In March 1782 the British House of Commons had voted in parliament with a No offensive war against America as a result of the surrender of Yorktown. News 
Title: History of the United States (1776–1789)
Content:  them, much of the territory they left dissolved into a chaotic guerrilla war, as the bands of Loyalists, one by one, were overwhelmed by the patriots. The British army under Lord Cornwallis marched to Yorktown, Virginia where they expected to be rescued by a British fleet. When that fleet was defeated by a French fleet, however, they were trapped and were surrounded by a much stronger force of Americans and French under Washington's command. On October 19, 1781, Cornwallis surrendered. News of the defeat effectively ended the fighting in America, although the naval war continued. Support for the conflict had never been strong in Britain, where many sympathized with the rebels, but now it reached a new low. King George III personally wanted to fight on, but he lost control of Parliament and had to agree to peace negotiations.
Title: Battle of Waxhaws
Content:  Following the British defeat at Saratoga in 1777 and French entry into the American Revolutionary War in early 1778, the British military decided to embark on a "southern strategy" to win back their rebellious colonies. The British believed they had more supporters in the South due to the close business and trading relationships, and that they might concentrate power in the South and later retake the North. They began the campaign in December 1778 with the capture of Savannah, Georgia. In 1780, General Sir Henry Clinton brought an army south and captured Charleston, South Carolina on May 12, 1780, after a siege.
Title: Harbor Defenses of New York
Content:  two years earlier. The military focus of the war shifted to the southern colonies. Eventually, the American victory in the Yorktown campaign on 19 October 1781 proved to be the key to independence; the British received word of it on 25 November. This precipitated a collapse of Lord North's Tory government in March 1782. The new Whig government suspended offensive operations in the Thirteen Colonies and commenced lengthy peace negotiations, culminating in the Treaty of Paris that ended the war on 3 September 1783. On 25 November the British forces departed New York City; this is remembered as Evacuation Day.

Question: which battle ended britain's support for the south?
Answer: Battle of Antietam.
the Battle of Antietam.