Founded by and for their states, public flagship universities are increasingly becoming national institutions with students from across the country. The University of Michigan at Ann Arbor shows the trend: Barely more than half of its incoming freshmen, 51 percent, were from within the state in fall 2016.

That was down 13 percentage points from a decade earlier.

The question of student’s home states is a huge issue for universities. For hundreds of thousands of college-bound students nationwide, their home-state flagship is either their top choice or one of them.

A Washington Post analysis of the latest available federal data found that at 11 flagships in 2016, more than half of the incoming freshman classes were from out of state. For several small states, that was no surprise. Those low-population states must recruit from throughout their regions to fill classes. The lowest in-state share, 21 percent, was at the University of Vermont.

Of the New England states, the University of Massachusetts Amherst had the highest percentage of in-state students, at 73 percent.

Some state schools have made a conscious decision to go national. A prime example is the University of Alabama, where 32 percent of freshmen in 2016 were from the state. That was down 34 points in a decade. Alabama, with its national powerhouse football team as a marketing draw, has exemplified the move toward out-of-state students.

At West Virginia University, the in-state share was 45 percent, down a few points over 10 years. But university President E. Gordon Gee said he wants to draw as many state residents as possible to the flagship campus in Morgantown. ‘‘Our future in West Virginia is to keep our talent in state,’’ he said.

Out-of-state students help universities in significant ways. They diversify campuses, bringing fresh perspectives and life experiences. They fill seats in states with stagnant or declining population. And of course, they pay more. In-state students at public universities get a huge discount on tuition. Those from elsewhere bring revenue that helps support that discount and offset the long decline in state funding for higher education. College Board data show that tuition and fees for in-state students at public universities this year average $9,970. For out-of-state students, the average is $25,620.

That’s a difference of nearly $16,000.

But there are drawbacks. Politically, it can be risky for prestigious schools to be perceived as giving too many seats to outsiders. And out-of-state students are often wealthier than those from in state, which can hinder efforts to foster socioeconomic diversity on campuses.

Consider the University of Michigan. It is one of the most prestigious universities in the country, public or private. It produces vast amounts of research and serves about 44,700 students. Nearly 29,000 are undergraduates. Of those undergrads, 15 percent come from families with enough financial need to qualify for Pell Grants. At many other public universities, the Pell share is twice or three times that. At the same time, Michigan’s in-state share of freshmen slid. It was 64 percent in 2006 and as high as 67 percent in 2008.

Mark Schlissel, president of the University of Michigan since July 2014, said in a recent visit to The Post that he wants to raise the Pell share and preserve the in-state majority on campus.

‘‘As a public university, we should be much more representative of all kinds of diversity,’’ he said.

Of Pell-eligible students, Schlissel said, he wants the percentage to be ‘‘over 20 at least before I’m done.’’

Of in-state students, he said: ‘‘I would like to keep the majority of undergrads from Michigan.’’

He said Michigan offers significant aid programs that ensure students from within the state can attend regardless of financial need.

The Post’s analysis found that the in-state share of freshmen rose at just 6 of the 50 flagships from 2006 to 2016. Those were the universities of Alaska, Delaware, Georgia, Idaho, Maryland, and Virginia.