It depends on many factors, but not all estates need to be probated.  
Assets, even large ones, can pass to heirs outside of the will.  Socks
simply made me beneficiary on his brokerage accounts, insurance policies
& the like.  Most 401Ks have that option. Some accounts even allow %
distribution to multiple beneficiaries.  Socks (finally) put me on his
bank acount, a huge help,  Before he did, the  bank wouldn't give me any
info about balances & he had some complex activities - money coming
in/going out automatically.  I needed to know so I could make sure
balances stayed positive.  A monthly statement wasn't enough. He wasn't
able to handle toward the end.

When ordering those death certificates, remember you might need one for
any contract you are breaking due to death - such as cell phone.  Some
took copies. Even one relatively small insurance policy paid with only a
copy.  Ditto car title transfer.  I have most left over but will keep
some at home & some in safe deposit box. You just never know who might
require one.  Safe deposit box: make sure surviving spouse is on the
record.  

You might want to check your credit card accounts to see that both
spouses are  owners, not just authorized users, for the ones you want to
keep.  Death notification goes to credit bureaus which are monitored by
credit card issuers. Socks  had a Discover card that was shut down with
no notification to me.  I was authorized user, but it was not a joint
account.  Thought about telling them to go get the money from him - then
thought again & paid it off :-)

I went through all the mail for a couple of months after diagnosis, just
to see if something needed to be changed so I would have access to it
without a lot of hassle.

Passwords - be sure you know them for ATM access, computers (many have
multiple). If you have DSL & have a power outage, you may need to enter a
code to get reconnected.  Do you know how to find it?  Do you know who
provides household services - plumber, lawn mowing company, painters,
roofers, carpet cleaners, pet sitters?  Do you have maintenance contracts
for anything - HVAC?  Anything under warranty?

Pay bills online?  You'll need login/passwords to access accounts.  
Receive paperless bills?  You need to know the drill.  How about ISP
providers, domain name registrations?  Web pages?  Someone needs to know
how all of this works.

Things to cancel (no need to continue paying for): car insurance for
deceased, coverage such as AAA, health club membership, dues, maybe
tithing, cell phone service, subscriptions to unwanted publications,
book/music clubs, professional organization membership & other
memberships (golf club, country club, travel club).

I hope this doesn't overwhelm.  I went through all of this with minimal
problems except for computer passwords.  There was plenty I didn't know
about his computers - one dual boot with Linux. It's so much easier to
maintain the status quo than to have to call everyone at once to get
changes made.

Fig