Inherited Tenants and dogs/ rent payments for closing

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Hi everyone, 

I am about to pick up a triplex and am about to close... The seller who is not well organized said they usually collect rents on the 5th (usually).. i close on the third of this month and had some questions about best practice... 

I told them that they should collect the rents that are due on the 1st and prorate the rents for the first couple days and deposit the residual rent into an escrow account...

They want me to collect the rents but I don't think this is a great idea... 

Any thoughts on this one?

Also, one of the tenants has 4 small dogs... The previous owner just let them have them without any pet addendum or collecting a security deposit... 

What would peoples approach be for this? I was thinking keep the tenants and pet and apply a security deposit when I have them re-sign the lease.

Thoughts on these?