A process called Service Host: Local System is using up all of my laptops resources

Something to note - I was experiencing a similar issue (CPU usage from service host was over 70%), but I noticed the process below it was an HP help process. I ended that, and my service host usage immediately dropped to 0%. Try closing superfluous HP processes and see if it does the trick. 

I've read through this entire topic.  I'm running Windows10 and having problems with

scannow found nothing and WindowsUpdate cannot be disabled (although it's a good idea to disable its file sharing process.)

My symptoms are that the network restricted group of processes grow gradually until they consume all of memory.  After about 4 days, the total private memory allocated to them is the largest of all processes and it continues to grow until other processes can no longer start due to resource limitations.

I did discover an HP driver process that was hogging the computer and have uninstalled my all-in-one to see if that helps.  Maybe now I can stop having to reboot every few days.

BTW, my computer does not sleep since I run a Distributed Computing project that keeps it busy 24x7.

Method 2 worked. Thanks.

YES!!!

You must open services.msc and disable the following:

background intelligence transfer service (BITS)

Windows update

update orchestrator

A couple things I didn't see in any of the responses so far (although I didn't read all of them) which you might want to check:

• Is Windows downloading any updates? Go to Settings area and check to see if it's in progress downloading the updates it does periodically (this was happening for me--had to install three updates that were downloading)
• Did it download an update and it wants to install it? Reboot and you'll know if this is the case. (And it's always a good idea to reboot anyway, especially if you're experiencing abnormal activity on a PC.
• Do you have any cloud storage services like Dropbox or Google Drive which are sync'ing? Check their status in the system tray (bottom right corner where all the little icons are). After I did my Windows updates, I had to pause Dropbox, which was downloading a lot of files I had added through my work PC the previous day). Between this and my Windows updates being up to date, my drive usage became normal again.
• Are any of your security programs (anti-virus or other similar services) performing scans in the background? This can also be seen in the system tray.

If you're checking something in the system tray to see if it's running a service, you can often just mouse over it and it will tell you what it's doing. 

Also, you can often pause these for a while and then check your Task Manager to see if that freed up your harddrive. Allow 2-3 minutes for the service to gracefully pause.

I'm on a Windows 10 machine and it's a desktop, but the above things would apply to any PC.

i strongly advise you AGAINST this solution

This will delete all your WiFi settings and internet passwords for them