I've seen people buy a rental property, not in their neighborhood but in other states with a lower cost of living. These houses usually are like $70k and they would rent it out via rental management so they get docked a fee out of their rent for the manager to take care of their property. How profitable is a venture like this even with the property manager fee I would imagine you can still make a decent chunk of change?
Having a management company take a cut out of every payment will make it harder to generate a profit each month based on the income from rent and the committed expenses for the mortgage, real estate taxes and other known items.
Having a management company does transfer the time requirement of responding to the care and maintenance of the property to the management company. The owner doesn't have to respond to a phone call in the middle of the night. If that property is hours away by car a management company will almost be required.
The cost of the management fee doesn't impact the gain in value of the property over the years. That means if the expected profits are to be mostly from growth in value then the need to make a profit each month isn't the driving factor, you are just waiting until the right time to sell.
You will have to do the research to determine if the expected rent on a 70K house in that region can support the required expenses and the cost of a property management contract.
I know that when I has a condo I couldn't sell, and had to rent it out, the monthly income would not have supported a property management contract. It was local so it wasn't required. But having one would have increased the losses each month.
To directly answer your question. A property manager will generally take about 8-10% of your monthly rent and 1-2 months rent for every time they find you a new tenant. That is the impact of not managing your own properties (whether in or out of state). If the other state has a state income tax you may also incur costs there (but not always).
As the other answer noted, "How Profitable" involves a thousand variables, but I'm guessing you are assuming landlords make much more money than they actually do on average. It's a good venture, but unless you have a ton of properties you aren't necessarily rolling in money.