The one-type-fits-all HD grass seed is a lower quality version in the one-type-fits-all grass seed category. The one-type-fits-all idea is to combine a shade loving grass like fescue with a sun loving grass like Kentucky bluegrass. What you get at HD, Lowe's, Walmart, etc., is a mix of grasses that might not be the mix you want and it likely has more contamination with weed and "other crop" seeds. If you order a custom mix of seeds from an online seed dealer you will get the colors you want, for example. Usually people try to get a deep green fescue and a deep green KBG. That kind of customization cannot be done at the big box stores. Another reason for mixing types of grass is that sometimes a pest or disease will come through that devastates one grass or another, but not both. The grass might not look excellent, but it might look greenish instead of bare. With that additional information, what do you want to do? Look online for grass seed dealers. You might also look for the NTEP grass test results for NJ.

Is there any reason why the grass near the tree would be thin? Does it not get the same amount of water? Or does it not get more water to account for the tree roots taking a share for the tree? What is your watering program? How often and for how long do you water?

How high/low do you mow?

When were the last two times you fertilized and what did you use?

Thanks for the advice; I will definitely follow it.

There is a swath of lawn from the northeast corner of the yard that hugs the edge and then moves out in front of the maple about 20' wide more or less following the drip line of the maple (the maple has extremely thick roots at the surface.) The grass starts lush in the Spring and then thins out as the summer progresses. This is about 20% of the total back lawn --- the rest of the lawn, except for the squirrel damage, is much better.

I water every other day for 1/2 hour using a series of oscillating sprinklers. I have a separate timer for the area around the maple for the lawn and for shade plants beneath it --- that gets another 1/2 hour at mid-day. I mow the lawn every 5 days at the 2nd highest setting on my lawn tractor (about 3+"). I use a pre-emergent in early Spring and weed control 8 weeks later both with fertilizer (Scott's). I do not fertilize in the Fall.