LeBuick said:
			
		
	
	
		
		
			I follow you now, Timothy was left in charge in Ephesus
 
1 Timothy 1:3 As I besought thee to abide still at Ephesus, when I went into Macedonia, that thou mightest charge some that they teach no other doctrine,
 
However, keep in mind, Ephesus was a large city, a Capitol city so many Chruches were formed. That might account for the multiple elders. We also know of Appolos having success there and Aquilla and Pricilla being leaders.
 
John is also said to have spent his last years there.
		
		
	 
 
In 1 Timothy 1;3, Paul delegated his authority as an apostle to Timothy to perform a specifie task as indicated: 
so that you may command certain men not to teach false doctrines any longer nor devote themselves to myths and endless genealogies. Timothy was not one of the elders in the church, but was there for a specific task authorized by the Apostle Paul and when he was done he moved on. In I Timothy chapter 3, Paul gives Timothy instructions on the qualifications of overseers that Timothy may have to appoint on behalf of Paul. After Timothy left, the group of elders ran the church as in other churches. Note that Timothy was not task to be an elder.
 
Paul gave the same type tasks to Titus. In Titus 1:5, 
The reason I left you in Crete was that you might straighten out what was left unfinished and appoint elders in every town, as I directed you. Note that elders (plural) were to be appointed in every town (every church).
 
IF a church had an apostle, the apostle was in charge of the church because he had first hand knowledge and experience concerning Jesus ministry. This is the reason why Paul devoted parts of his letters to establish himself as an apostle. Paul had the authority of an apostle like the other apostles. He delegated that authority to Timothy and Titus for specific tasks.
 
Concerning many churches in Ephesus, granted they probably met in small groups most of the time due to facility limitations. However, these groups probably had more than one elder since we know that small churches (Titus 1;5) had plural elders. Again, had there been a leader among elders at Ephesus, he would have been mentioned in Acts 20:17-36.
 
The N.T. churches had a group of elders that were in charge of the church if no apostles were present.